diff --git a/src/Symfony/Component/Scheduler/CHANGELOG.md b/src/Symfony/Component/Scheduler/CHANGELOG.md
index 368d423136680..a8de099be3dd4 100644
--- a/src/Symfony/Component/Scheduler/CHANGELOG.md
+++ b/src/Symfony/Component/Scheduler/CHANGELOG.md
@@ -7,6 +7,7 @@ CHANGELOG
  * Allow setting timezone of next run date in CronExpressionTrigger
  * Add `AbstractTriggerDecorator`
  * Make `ScheduledStamp` "send-able"
+ * Add `ScheduledStamp` to `RedispatchMessage`
 
 6.3
 ---
diff --git a/src/Symfony/Component/Scheduler/Messenger/SchedulerTransport.php b/src/Symfony/Component/Scheduler/Messenger/SchedulerTransport.php
index 414945e617c83..f8e7d973c4e26 100644
--- a/src/Symfony/Component/Scheduler/Messenger/SchedulerTransport.php
+++ b/src/Symfony/Component/Scheduler/Messenger/SchedulerTransport.php
@@ -12,6 +12,7 @@
 namespace Symfony\Component\Scheduler\Messenger;
 
 use Symfony\Component\Messenger\Envelope;
+use Symfony\Component\Messenger\Message\RedispatchMessage;
 use Symfony\Component\Messenger\Transport\TransportInterface;
 use Symfony\Component\Scheduler\Exception\LogicException;
 use Symfony\Component\Scheduler\Generator\MessageGeneratorInterface;
@@ -29,7 +30,16 @@ public function __construct(
     public function get(): iterable
     {
         foreach ($this->messageGenerator->getMessages() as $context => $message) {
-            yield Envelope::wrap($message, [new ScheduledStamp($context)]);
+            $stamp = new ScheduledStamp($context);
+
+            if ($message instanceof RedispatchMessage) {
+                $message = new RedispatchMessage(
+                    Envelope::wrap($message->envelope, [$stamp]),
+                    $message->transportNames,
+                );
+            }
+
+            yield Envelope::wrap($message, [$stamp]);
         }
     }
 
diff --git a/src/Symfony/Component/Scheduler/Tests/Messenger/SchedulerTransportTest.php b/src/Symfony/Component/Scheduler/Tests/Messenger/SchedulerTransportTest.php
index d4294ec470dad..40b1cd9cbe669 100644
--- a/src/Symfony/Component/Scheduler/Tests/Messenger/SchedulerTransportTest.php
+++ b/src/Symfony/Component/Scheduler/Tests/Messenger/SchedulerTransportTest.php
@@ -13,6 +13,7 @@
 
 use PHPUnit\Framework\TestCase;
 use Symfony\Component\Messenger\Envelope;
+use Symfony\Component\Messenger\Message\RedispatchMessage;
 use Symfony\Component\Scheduler\Exception\LogicException;
 use Symfony\Component\Scheduler\Generator\MessageContext;
 use Symfony\Component\Scheduler\Generator\MessageGeneratorInterface;
@@ -28,9 +29,7 @@ public function testGetFromIterator()
             (object) ['id' => 'first'],
             (object) ['id' => 'second'],
         ];
-        $generator = $this->createMock(MessageGeneratorInterface::class, [
-            'getMessages' => $messages,
-        ]);
+        $generator = $this->createMock(MessageGeneratorInterface::class);
         $generator->method('getMessages')->willReturnCallback(function () use ($messages): \Generator {
             $trigger = $this->createMock(TriggerInterface::class);
             $triggerAt = new \DateTimeImmutable('2020-02-20T02:00:00', new \DateTimeZone('UTC'));
@@ -50,6 +49,22 @@ public function testGetFromIterator()
         $this->assertEmpty($messages);
     }
 
+    public function testAddsStampToInnerRedispatchMessageEnvelope()
+    {
+        $generator = $this->createMock(MessageGeneratorInterface::class);
+        $generator->method('getMessages')->willReturnCallback(function (): \Generator {
+            yield new MessageContext('default', 'id', $this->createMock(TriggerInterface::class), new \DateTimeImmutable()) =>
+                new RedispatchMessage(new \stdClass(), ['transport']);
+        });
+        $envelopes = \iterator_to_array((new SchedulerTransport($generator))->get());
+
+        $stamp = $envelopes[0]->getMessage()->envelope->last(ScheduledStamp::class);
+
+        $this->assertSame($stamp, $envelopes[0]->last(ScheduledStamp::class));
+        $this->assertSame('default', $stamp->messageContext->name);
+        $this->assertSame('id', $stamp->messageContext->id);
+    }
+
     public function testAckIgnored()
     {
         $transport = new SchedulerTransport($this->createMock(MessageGeneratorInterface::class));