diff --git a/assets/l10n/app_en.arb b/assets/l10n/app_en.arb
index b0152fc28e..2ce7b9f011 100644
--- a/assets/l10n/app_en.arb
+++ b/assets/l10n/app_en.arb
@@ -43,10 +43,14 @@
   "@permissionsDeniedReadExternalStorage": {
     "description": "Message for dialog asking the user to grant permissions for external storage read access."
   },
-  "actionSheetOptionCopy": "Copy message text",
-  "@actionSheetOptionCopy":  {
+  "actionSheetOptionCopyMessageText": "Copy message text",
+  "@actionSheetOptionCopyMessageText":  {
     "description": "Label for copy message text button on action sheet."
   },
+  "actionSheetOptionCopyMessageLink": "Copy link to message",
+  "@actionSheetOptionCopyMessageLink": {
+    "description": "Label for copy message link button on action sheet."
+  },
   "actionSheetOptionShare": "Share",
   "@actionSheetOptionShare":  {
     "description": "Label for share button on action sheet."
@@ -168,10 +172,14 @@
   "@successLinkCopied": {
     "description": "Success message after copy link action completed."
   },
-  "successMessageCopied": "Message Copied",
-  "@successMessageCopied": {
+  "successMessageTextCopied": "Message text copied",
+  "@successMessageTextCopied": {
     "description": "Message when content of a message was copied to the user's system clipboard."
   },
+  "successMessageLinkCopied": "Message link copied",
+  "@successMessageLinkCopied": {
+    "description": "Message when link of a message was copied to the user's system clipboard."
+  },
   "composeBoxAttachFilesTooltip": "Attach files",
   "@composeBoxAttachFilesTooltip": {
     "description": "Tooltip for compose box icon to attach a file to the message."
diff --git a/lib/widgets/action_sheet.dart b/lib/widgets/action_sheet.dart
index 424d666016..b224d74769 100644
--- a/lib/widgets/action_sheet.dart
+++ b/lib/widgets/action_sheet.dart
@@ -6,6 +6,8 @@ import 'package:share_plus/share_plus.dart';
 import '../api/exception.dart';
 import '../api/model/model.dart';
 import '../api/route/messages.dart';
+import '../model/internal_link.dart';
+import '../model/narrow.dart';
 import 'clipboard.dart';
 import 'compose_box.dart';
 import 'dialog.dart';
@@ -39,12 +41,13 @@ void showMessageActionSheet({required BuildContext context, required Message mes
       return Column(children: [
         if (!hasThumbsUpReactionVote) AddThumbsUpButton(message: message, messageListContext: context),
         StarButton(message: message, messageListContext: context),
-        ShareButton(message: message, messageListContext: context),
         if (isComposeBoxOffered) QuoteAndReplyButton(
           message: message,
           messageListContext: context,
         ),
-        CopyButton(message: message, messageListContext: context),
+        CopyMessageTextButton(message: message, messageListContext: context),
+        CopyMessageLinkButton(message: message, messageListContext: context),
+        ShareButton(message: message, messageListContext: context),
       ]);
     });
 }
@@ -164,63 +167,6 @@ class StarButton extends MessageActionSheetMenuItemButton {
   }
 }
 
-class ShareButton extends MessageActionSheetMenuItemButton {
-  ShareButton({
-    super.key,
-    required super.message,
-    required super.messageListContext,
-  });
-
-  @override IconData get icon => Icons.adaptive.share;
-
-  @override
-  String label(ZulipLocalizations zulipLocalizations) {
-    return zulipLocalizations.actionSheetOptionShare;
-  }
-
-  @override void onPressed(BuildContext context) async {
-    // Close the message action sheet; we're about to show the share
-    // sheet. (We could do this after the sharing Future settles
-    // with [ShareResultStatus.success], but on iOS I get impatient with
-    // how slowly our action sheet dismisses in that case.)
-    // TODO(#24): Fix iOS bug where this call causes the keyboard to
-    //   reopen (if it was open at the time of this
-    //   `showMessageActionSheet` call) and cover a large part of the
-    //   share sheet.
-    Navigator.of(context).pop();
-    final zulipLocalizations = ZulipLocalizations.of(messageListContext);
-
-    final rawContent = await fetchRawContentWithFeedback(
-      context: messageListContext,
-      messageId: message.id,
-      errorDialogTitle: zulipLocalizations.errorSharingFailed,
-    );
-
-    if (rawContent == null) return;
-
-    if (!messageListContext.mounted) return;
-
-    // TODO: to support iPads, we're asked to give a
-    //   `sharePositionOrigin` param, or risk crashing / hanging:
-    //     https://pub.dev/packages/share_plus#ipad
-    //   Perhaps a wart in the API; discussion:
-    //     https://github.com/zulip/zulip-flutter/pull/12#discussion_r1130146231
-    final result = await Share.share(rawContent);
-
-    switch (result.status) {
-      // The plugin isn't very helpful: "The status can not be determined".
-      // Until we learn otherwise, assume something wrong happened.
-      case ShareResultStatus.unavailable:
-        if (!messageListContext.mounted) return;
-        await showErrorDialog(context: messageListContext,
-          title: zulipLocalizations.errorSharingFailed);
-      case ShareResultStatus.success:
-      case ShareResultStatus.dismissed:
-        // nothing to do
-    }
-  }
-}
-
 /// Fetch and return the raw Markdown content for [messageId],
 /// showing an error dialog on failure.
 Future<String?> fetchRawContentWithFeedback({
@@ -330,8 +276,8 @@ class QuoteAndReplyButton extends MessageActionSheetMenuItemButton {
   }
 }
 
-class CopyButton extends MessageActionSheetMenuItemButton {
-  CopyButton({
+class CopyMessageTextButton extends MessageActionSheetMenuItemButton {
+  CopyMessageTextButton({
     super.key,
     required super.message,
     required super.messageListContext,
@@ -341,7 +287,7 @@ class CopyButton extends MessageActionSheetMenuItemButton {
 
   @override
   String label(ZulipLocalizations zulipLocalizations) {
-    return zulipLocalizations.actionSheetOptionCopy;
+    return zulipLocalizations.actionSheetOptionCopyMessageText;
   }
 
   @override void onPressed(BuildContext context) async {
@@ -361,8 +307,96 @@ class CopyButton extends MessageActionSheetMenuItemButton {
 
     if (!messageListContext.mounted) return;
 
-    copyWithPopup(context: context,
-      successContent: Text(zulipLocalizations.successMessageCopied),
+    copyWithPopup(context: messageListContext,
+      successContent: Text(zulipLocalizations.successMessageTextCopied),
       data: ClipboardData(text: rawContent));
   }
 }
+
+class CopyMessageLinkButton extends MessageActionSheetMenuItemButton {
+  CopyMessageLinkButton({
+    super.key,
+    required super.message,
+    required super.messageListContext,
+  });
+
+  @override IconData get icon => Icons.link;
+
+  @override
+  String label(ZulipLocalizations zulipLocalizations) {
+    return zulipLocalizations.actionSheetOptionCopyMessageLink;
+  }
+
+  @override void onPressed(BuildContext context) {
+    Navigator.of(context).pop();
+    final zulipLocalizations = ZulipLocalizations.of(messageListContext);
+
+    final store = PerAccountStoreWidget.of(messageListContext);
+    final messageLink = narrowLink(
+      store,
+      SendableNarrow.ofMessage(message, selfUserId: store.selfUserId),
+      nearMessageId: message.id,
+    );
+
+    copyWithPopup(context: messageListContext,
+      successContent: Text(zulipLocalizations.successMessageLinkCopied),
+      data: ClipboardData(text: messageLink.toString()));
+  }
+}
+
+class ShareButton extends MessageActionSheetMenuItemButton {
+  ShareButton({
+    super.key,
+    required super.message,
+    required super.messageListContext,
+  });
+
+  @override IconData get icon => Icons.adaptive.share;
+
+  @override
+  String label(ZulipLocalizations zulipLocalizations) {
+    return zulipLocalizations.actionSheetOptionShare;
+  }
+
+  @override void onPressed(BuildContext context) async {
+    // Close the message action sheet; we're about to show the share
+    // sheet. (We could do this after the sharing Future settles
+    // with [ShareResultStatus.success], but on iOS I get impatient with
+    // how slowly our action sheet dismisses in that case.)
+    // TODO(#24): Fix iOS bug where this call causes the keyboard to
+    //   reopen (if it was open at the time of this
+    //   `showMessageActionSheet` call) and cover a large part of the
+    //   share sheet.
+    Navigator.of(context).pop();
+    final zulipLocalizations = ZulipLocalizations.of(messageListContext);
+
+    final rawContent = await fetchRawContentWithFeedback(
+      context: messageListContext,
+      messageId: message.id,
+      errorDialogTitle: zulipLocalizations.errorSharingFailed,
+    );
+
+    if (rawContent == null) return;
+
+    if (!messageListContext.mounted) return;
+
+    // TODO: to support iPads, we're asked to give a
+    //   `sharePositionOrigin` param, or risk crashing / hanging:
+    //     https://pub.dev/packages/share_plus#ipad
+    //   Perhaps a wart in the API; discussion:
+    //     https://github.com/zulip/zulip-flutter/pull/12#discussion_r1130146231
+    final result = await Share.share(rawContent);
+
+    switch (result.status) {
+      // The plugin isn't very helpful: "The status can not be determined".
+      // Until we learn otherwise, assume something wrong happened.
+      case ShareResultStatus.unavailable:
+        if (!messageListContext.mounted) return;
+        await showErrorDialog(context: messageListContext,
+          title: zulipLocalizations.errorSharingFailed);
+      case ShareResultStatus.success:
+      case ShareResultStatus.dismissed:
+        // nothing to do
+    }
+  }
+}
diff --git a/test/widgets/action_sheet_test.dart b/test/widgets/action_sheet_test.dart
index a006fa640f..9b654eb4ff 100644
--- a/test/widgets/action_sheet_test.dart
+++ b/test/widgets/action_sheet_test.dart
@@ -8,7 +8,9 @@ import 'package:flutter_test/flutter_test.dart';
 import 'package:http/http.dart' as http;
 import 'package:zulip/api/model/model.dart';
 import 'package:zulip/api/route/messages.dart';
+import 'package:zulip/model/binding.dart';
 import 'package:zulip/model/compose.dart';
+import 'package:zulip/model/internal_link.dart';
 import 'package:zulip/model/localizations.dart';
 import 'package:zulip/model/narrow.dart';
 import 'package:zulip/model/store.dart';
@@ -84,11 +86,12 @@ void main() {
   void prepareRawContentResponseSuccess(PerAccountStore store, {
     required Message message,
     required String rawContent,
+    Duration delay = Duration.zero,
   }) {
     // Prepare fetch-raw-Markdown response
     // TODO: Message should really only differ from `message`
     //   in its content / content_type, not in `id` or anything else.
-    (store.connection as FakeApiConnection).prepare(json:
+    (store.connection as FakeApiConnection).prepare(delay: delay, json:
       GetMessageResult(message: eg.streamMessage(contentMarkdown: rawContent)).toJson());
   }
 
@@ -245,70 +248,6 @@ void main() {
     });
   });
 
-  group('ShareButton', () {
-    // Tests should call this.
-    MockSharePlus setupMockSharePlus() {
-      final mock = MockSharePlus();
-      TestDefaultBinaryMessengerBinding.instance.defaultBinaryMessenger.setMockMethodCallHandler(
-        MethodChannelShare.channel,
-        mock.handleMethodCall,
-      );
-      return mock;
-    }
-
-    Future<void> tapShareButton(WidgetTester tester) async {
-      await tester.ensureVisible(find.byIcon(Icons.adaptive.share, skipOffstage: false));
-      await tester.tap(find.byIcon(Icons.adaptive.share));
-      await tester.pump(); // [MenuItemButton.onPressed] called in a post-frame callback: flutter/flutter@e4a39fa2e
-    }
-
-    testWidgets('request succeeds; sharing succeeds', (WidgetTester tester) async {
-      final mockSharePlus = setupMockSharePlus();
-      final message = eg.streamMessage();
-      await setupToMessageActionSheet(tester, message: message, narrow: TopicNarrow.ofMessage(message));
-      final store = await testBinding.globalStore.perAccount(eg.selfAccount.id);
-
-      prepareRawContentResponseSuccess(store, message: message, rawContent: 'Hello world');
-      await tapShareButton(tester);
-      await tester.pump(Duration.zero);
-      check(mockSharePlus.sharedString).equals('Hello world');
-    });
-
-    testWidgets('request succeeds; sharing fails', (WidgetTester tester) async {
-      final mockSharePlus = setupMockSharePlus();
-      final message = eg.streamMessage();
-      await setupToMessageActionSheet(tester, message: message, narrow: TopicNarrow.ofMessage(message));
-      final store = await testBinding.globalStore.perAccount(eg.selfAccount.id);
-
-      prepareRawContentResponseSuccess(store, message: message, rawContent: 'Hello world');
-      mockSharePlus.resultString = 'dev.fluttercommunity.plus/share/unavailable';
-      await tapShareButton(tester);
-      await tester.pump(Duration.zero);
-      check(mockSharePlus.sharedString).equals('Hello world');
-      await tester.pump();
-      await tester.tap(find.byWidget(checkErrorDialog(tester,
-        expectedTitle: 'Sharing failed')));
-    });
-
-    testWidgets('request has an error', (WidgetTester tester) async {
-      final mockSharePlus = setupMockSharePlus();
-      final message = eg.streamMessage();
-      await setupToMessageActionSheet(tester, message: message, narrow: TopicNarrow.ofMessage(message));
-      final store = await testBinding.globalStore.perAccount(eg.selfAccount.id);
-
-      prepareRawContentResponseError(store);
-      await tapShareButton(tester);
-      await tester.pump(Duration.zero); // error arrives; error dialog shows
-
-      await tester.tap(find.byWidget(checkErrorDialog(tester,
-        expectedTitle: 'Sharing failed',
-        expectedMessage: 'That message does not seem to exist.',
-      )));
-
-      check(mockSharePlus.sharedString).isNull();
-    });
-  });
-
   group('QuoteAndReplyButton', () {
     ComposeBoxController? findComposeBoxController(WidgetTester tester) {
       return tester.widget<ComposeBox>(find.byType(ComposeBox))
@@ -449,7 +388,7 @@ void main() {
     });
   });
 
-  group('CopyButton', () {
+  group('CopyMessageTextButton', () {
     setUp(() async {
       TestDefaultBinaryMessengerBinding.instance.defaultBinaryMessenger.setMockMethodCallHandler(
         SystemChannels.platform,
@@ -457,7 +396,7 @@ void main() {
       );
     });
 
-    Future<void> tapCopyButton(WidgetTester tester) async {
+    Future<void> tapCopyMessageTextButton(WidgetTester tester) async {
       await tester.ensureVisible(find.byIcon(Icons.copy, skipOffstage: false));
       await tester.tap(find.byIcon(Icons.copy));
       await tester.pump(); // [MenuItemButton.onPressed] called in a post-frame callback: flutter/flutter@e4a39fa2e
@@ -469,18 +408,43 @@ void main() {
       final store = await testBinding.globalStore.perAccount(eg.selfAccount.id);
 
       prepareRawContentResponseSuccess(store, message: message, rawContent: 'Hello world');
-      await tapCopyButton(tester);
+      await tapCopyMessageTextButton(tester);
       await tester.pump(Duration.zero);
       check(await Clipboard.getData('text/plain')).isNotNull().text.equals('Hello world');
     });
 
+    testWidgets('can show snackbar on success', (tester) async {
+      // Regression test for: https://github.com/zulip/zulip-flutter/issues/732
+      testBinding.deviceInfoResult = IosDeviceInfo(systemVersion: '16.0');
+
+      final message = eg.streamMessage();
+      await setupToMessageActionSheet(tester, message: message, narrow: TopicNarrow.ofMessage(message));
+      final store = await testBinding.globalStore.perAccount(eg.selfAccount.id);
+
+      // Make the request take a bit of time to complete…
+      prepareRawContentResponseSuccess(store, message: message, rawContent: 'Hello world',
+        delay: const Duration(milliseconds: 500));
+      await tapCopyMessageTextButton(tester);
+      // … and pump a frame to finish the NavigationState.pop animation…
+      await tester.pump(const Duration(milliseconds: 250));
+      // … before the request finishes.  This is the repro condition for #732.
+      await tester.pump(const Duration(milliseconds: 250));
+
+      final snackbar = tester.widget<SnackBar>(find.byType(SnackBar));
+      check(snackbar.behavior).equals(SnackBarBehavior.floating);
+      final zulipLocalizations = GlobalLocalizations.zulipLocalizations;
+      tester.widget(find.descendant(matchRoot: true,
+        of: find.byWidget(snackbar.content),
+        matching: find.text(zulipLocalizations.successMessageTextCopied)));
+    });
+
     testWidgets('request has an error', (WidgetTester tester) async {
       final message = eg.streamMessage();
       await setupToMessageActionSheet(tester, message: message, narrow: TopicNarrow.ofMessage(message));
       final store = await testBinding.globalStore.perAccount(eg.selfAccount.id);
 
       prepareRawContentResponseError(store);
-      await tapCopyButton(tester);
+      await tapCopyMessageTextButton(tester);
       await tester.pump(Duration.zero); // error arrives; error dialog shows
 
       await tester.tap(find.byWidget(checkErrorDialog(tester,
@@ -490,4 +454,95 @@ void main() {
       check(await Clipboard.getData('text/plain')).isNull();
     });
   });
+
+  group('CopyMessageLinkButton', () {
+    setUp(() async {
+      TestDefaultBinaryMessengerBinding.instance.defaultBinaryMessenger.setMockMethodCallHandler(
+        SystemChannels.platform,
+        MockClipboard().handleMethodCall,
+      );
+    });
+
+    Future<void> tapCopyMessageLinkButton(WidgetTester tester) async {
+      await tester.ensureVisible(find.byIcon(Icons.link, skipOffstage: false));
+      await tester.tap(find.byIcon(Icons.link));
+      await tester.pump(); // [MenuItemButton.onPressed] called in a post-frame callback: flutter/flutter@e4a39fa2e
+    }
+
+    testWidgets('copies message link to clipboard', (tester) async {
+      final message = eg.streamMessage();
+      final narrow = TopicNarrow.ofMessage(message);
+      await setupToMessageActionSheet(tester, message: message, narrow: narrow);
+      final store = await testBinding.globalStore.perAccount(eg.selfAccount.id);
+
+      await tapCopyMessageLinkButton(tester);
+      await tester.pump(Duration.zero);
+      final expectedLink = narrowLink(store, narrow, nearMessageId: message.id).toString();
+      check(await Clipboard.getData('text/plain')).isNotNull().text.equals(expectedLink);
+    });
+  });
+
+  group('ShareButton', () {
+    // Tests should call this.
+    MockSharePlus setupMockSharePlus() {
+      final mock = MockSharePlus();
+      TestDefaultBinaryMessengerBinding.instance.defaultBinaryMessenger.setMockMethodCallHandler(
+        MethodChannelShare.channel,
+        mock.handleMethodCall,
+      );
+      return mock;
+    }
+
+    Future<void> tapShareButton(WidgetTester tester) async {
+      await tester.ensureVisible(find.byIcon(Icons.adaptive.share, skipOffstage: false));
+      await tester.tap(find.byIcon(Icons.adaptive.share));
+      await tester.pump(); // [MenuItemButton.onPressed] called in a post-frame callback: flutter/flutter@e4a39fa2e
+    }
+
+    testWidgets('request succeeds; sharing succeeds', (WidgetTester tester) async {
+      final mockSharePlus = setupMockSharePlus();
+      final message = eg.streamMessage();
+      await setupToMessageActionSheet(tester, message: message, narrow: TopicNarrow.ofMessage(message));
+      final store = await testBinding.globalStore.perAccount(eg.selfAccount.id);
+
+      prepareRawContentResponseSuccess(store, message: message, rawContent: 'Hello world');
+      await tapShareButton(tester);
+      await tester.pump(Duration.zero);
+      check(mockSharePlus.sharedString).equals('Hello world');
+    });
+
+    testWidgets('request succeeds; sharing fails', (WidgetTester tester) async {
+      final mockSharePlus = setupMockSharePlus();
+      final message = eg.streamMessage();
+      await setupToMessageActionSheet(tester, message: message, narrow: TopicNarrow.ofMessage(message));
+      final store = await testBinding.globalStore.perAccount(eg.selfAccount.id);
+
+      prepareRawContentResponseSuccess(store, message: message, rawContent: 'Hello world');
+      mockSharePlus.resultString = 'dev.fluttercommunity.plus/share/unavailable';
+      await tapShareButton(tester);
+      await tester.pump(Duration.zero);
+      check(mockSharePlus.sharedString).equals('Hello world');
+      await tester.pump();
+      await tester.tap(find.byWidget(checkErrorDialog(tester,
+        expectedTitle: 'Sharing failed')));
+    });
+
+    testWidgets('request has an error', (WidgetTester tester) async {
+      final mockSharePlus = setupMockSharePlus();
+      final message = eg.streamMessage();
+      await setupToMessageActionSheet(tester, message: message, narrow: TopicNarrow.ofMessage(message));
+      final store = await testBinding.globalStore.perAccount(eg.selfAccount.id);
+
+      prepareRawContentResponseError(store);
+      await tapShareButton(tester);
+      await tester.pump(Duration.zero); // error arrives; error dialog shows
+
+      await tester.tap(find.byWidget(checkErrorDialog(tester,
+        expectedTitle: 'Sharing failed',
+        expectedMessage: 'That message does not seem to exist.',
+      )));
+
+      check(mockSharePlus.sharedString).isNull();
+    });
+  });
 }