diff --git a/swh/journal/replay.py b/swh/journal/replay.py
--- a/swh/journal/replay.py
+++ b/swh/journal/replay.py
@@ -4,8 +4,9 @@
 # See top-level LICENSE file for more information
 
 import copy
-from time import time
 import logging
+from time import time
+from typing import Callable, Dict, List, Optional
 
 try:
     from systemd.daemon import notify
@@ -16,7 +17,7 @@
 from swh.model.identifiers import normalize_timestamp
 from swh.model.hashutil import hash_to_hex
 from swh.model.model import SHA1_SIZE
-from swh.objstorage.objstorage import ID_HASH_ALGO
+from swh.objstorage.objstorage import ID_HASH_ALGO, ObjStorage
 from swh.storage import HashCollision
 
 logger = logging.getLogger(__name__)
@@ -321,8 +322,14 @@
     return len(obj)
 
 
-def process_replay_objects_content(all_objects, *, src, dst,
-                                   exclude_fn=None, check_dst=True):
+def process_replay_objects_content(
+        all_objects: Dict[str, List[dict]],
+        *,
+        src: ObjStorage,
+        dst: ObjStorage,
+        exclude_fn: Optional[Callable[[dict], bool]] = None,
+        check_dst: bool = True,
+):
     """
     Takes a list of records from Kafka (see
     :py:func:`swh.journal.client.JournalClient.process`) and copies them
@@ -330,15 +337,17 @@
 
     * `obj['status']` is `'visible'`
     * `exclude_fn(obj)` is `False` (if `exclude_fn` is provided)
+    * `obj['sha1'] not in dst` (if `check_dst` is True)
 
     Args:
-        all_objects Dict[str, List[dict]]: Objects passed by the Kafka client.
-            Most importantly, `all_objects['content'][*]['sha1']` is the
-            sha1 hash of each content
+        all_objects: Objects passed by the Kafka client. Most importantly,
+            `all_objects['content'][*]['sha1']` is the sha1 hash of each
+            content.
         src: An object storage (see :py:func:`swh.objstorage.get_objstorage`)
         dst: An object storage (see :py:func:`swh.objstorage.get_objstorage`)
-        exclude_fn Optional[Callable[dict, bool]]: Determines whether
-            an object should be copied.
+        exclude_fn: Determines whether an object should be copied.
+        check_dst: Determines whether we should check the destination
+            objstorage before copying.
 
     Example: