diff --git a/moto/sqs/models.py b/moto/sqs/models.py
index 5b0f5f430..421a1e5c7 100644
--- a/moto/sqs/models.py
+++ b/moto/sqs/models.py
@@ -818,8 +818,6 @@ class SQSBackend(BaseBackend):
                         # A previous call is still processing messages in this group, so we cannot deliver this one.
                         continue
 
-                queue.pending_messages.add(message)
-
                 if (
                     queue.dead_letter_queue is not None
                     and message.approximate_receive_count
@@ -828,6 +826,7 @@ class SQSBackend(BaseBackend):
                     messages_to_dlq.append(message)
                     continue
 
+                queue.pending_messages.add(message)
                 message.mark_received(visibility_timeout=visibility_timeout)
                 _filter_message_attributes(message, message_attribute_names)
                 result.append(message)
diff --git a/tests/test_sqs/test_sqs.py b/tests/test_sqs/test_sqs.py
index df7b8dec8..b7cbc793a 100644
--- a/tests/test_sqs/test_sqs.py
+++ b/tests/test_sqs/test_sqs.py
@@ -2384,3 +2384,42 @@ def test_fifo_queue_send_deduplicationid_same_as_sha256_of_old_message():
     )
     messages = msg_queue.receive_messages(MaxNumberOfMessages=2)
     messages.should.have.length_of(1)
+
+
+@mock_sqs
+def test_fifo_send_message_when_same_group_id_is_in_dlq():
+
+    sqs = boto3.resource("sqs", region_name="us-east-1")
+    dlq = sqs.create_queue(
+        QueueName="test-queue-dlq.fifo", Attributes={"FifoQueue": "true"}
+    )
+
+    queue = sqs.get_queue_by_name(QueueName="test-queue-dlq.fifo")
+    dead_letter_queue_arn = queue.attributes.get("QueueArn")
+
+    msg_queue = sqs.create_queue(
+        QueueName="test-queue.fifo",
+        Attributes={
+            "FifoQueue": "true",
+            "RedrivePolicy": json.dumps(
+                {"deadLetterTargetArn": dead_letter_queue_arn, "maxReceiveCount": 1},
+            ),
+            "VisibilityTimeout": "1",
+        },
+    )
+
+    msg_queue.send_message(MessageBody="first", MessageGroupId="1")
+    messages = msg_queue.receive_messages()
+    messages.should.have.length_of(1)
+
+    time.sleep(1.1)
+
+    messages = msg_queue.receive_messages()
+    messages.should.have.length_of(0)
+
+    messages = dlq.receive_messages()
+    messages.should.have.length_of(1)
+
+    msg_queue.send_message(MessageBody="second", MessageGroupId="1")
+    messages = msg_queue.receive_messages()
+    messages.should.have.length_of(1)