diff --git a/src/proto_alpha/lib_protocol/sc_rollup_arith.ml b/src/proto_alpha/lib_protocol/sc_rollup_arith.ml
index 03b63b573a837602a269b890d08c44694492463c..3aa81fec1a77bf05c831ddb53e90c3d8b6c19452 100644
--- a/src/proto_alpha/lib_protocol/sc_rollup_arith.ml
+++ b/src/proto_alpha/lib_protocol/sc_rollup_arith.ml
@@ -923,18 +923,20 @@ module Make (Context : P) :
 
   let set_inbox_message_monadic {PS.inbox_level; message_counter; payload} =
     let open Monad.Syntax in
-    let payload =
+    let* payload =
       match Sc_rollup_inbox_message_repr.deserialize payload with
-      | Error _ -> None
-      | Ok (External payload) -> Some payload
-      | Ok (Internal internal_inbox_message) -> (
-          match internal_inbox_message with
-          | Transfer {payload; _} -> (
+      | Error _ -> return None
+      | Ok (External payload) -> return (Some payload)
+      | Ok (Internal (Transfer {payload; destination; _})) -> (
+          let* (metadata : Sc_rollup_metadata_repr.t option) = Metadata.get in
+          match metadata with
+          | Some {address; _} when Address.(destination = address) -> (
               match Micheline.root payload with
-              | String (_, payload) -> Some payload
-              | _ -> None)
-          | Start_of_level -> None
-          | End_of_level -> None)
+              | String (_, payload) -> return (Some payload)
+              | _ -> return None)
+          | _ -> return None)
+      | Ok (Internal Start_of_level) -> return None
+      | Ok (Internal End_of_level) -> return None
     in
     match payload with
     | Some payload ->
diff --git a/src/proto_alpha/lib_protocol/sc_rollup_management_protocol.ml b/src/proto_alpha/lib_protocol/sc_rollup_management_protocol.ml
index 64912410b59b7fe6f1ecbcd731883fe1fcec045a..7b73c746c28203e1d4dc2d0db30a4dd055fcad06 100644
--- a/src/proto_alpha/lib_protocol/sc_rollup_management_protocol.ml
+++ b/src/proto_alpha/lib_protocol/sc_rollup_management_protocol.ml
@@ -54,7 +54,7 @@ type atomic_transaction_batch = {transactions : transaction list}
 
 type outbox_message = Atomic_transaction_batch of atomic_transaction_batch
 
-let make_internal_deposit ctxt ty ~payload ~sender ~source ~destination =
+let make_internal_transfer ctxt ty ~payload ~sender ~source ~destination =
   let open Lwt_tzresult_syntax in
   let+ payload, ctxt =
     Script_ir_translator.unparse_data
diff --git a/src/proto_alpha/lib_protocol/sc_rollup_management_protocol.mli b/src/proto_alpha/lib_protocol/sc_rollup_management_protocol.mli
index a313dd35f21948249a91ca9654f998604ed15cbc..d84cb3dc9b855a6ba4a000134b7b34ac152800dc 100644
--- a/src/proto_alpha/lib_protocol/sc_rollup_management_protocol.mli
+++ b/src/proto_alpha/lib_protocol/sc_rollup_management_protocol.mli
@@ -60,10 +60,10 @@ type atomic_transaction_batch = private {transactions : transaction list}
 type outbox_message = private
   | Atomic_transaction_batch of atomic_transaction_batch
 
-(** [make_internal_deposit ctxt ty ~payload ~sender ~source ~destination]
+(** [make_internal_transfer ctxt ty ~payload ~sender ~source ~destination]
     constructs a smart rollup's [inbox message] (an L1 to L2 message)
     with the given [payload], [sender], and [source] targeting [destination]. *)
-val make_internal_deposit :
+val make_internal_transfer :
   context ->
   ('a, _) Script_typed_ir.ty ->
   payload:'a ->
diff --git a/src/proto_alpha/lib_protocol/test/unit/test_sc_rollup_arith.ml b/src/proto_alpha/lib_protocol/test/unit/test_sc_rollup_arith.ml
index 8ee0e35eb9261f940a1e9fddb9ed1afae7b10ecb..d2d7192fd8e3e32845767c107f869c7feb7f0512 100644
--- a/src/proto_alpha/lib_protocol/test/unit/test_sc_rollup_arith.ml
+++ b/src/proto_alpha/lib_protocol/test/unit/test_sc_rollup_arith.ml
@@ -438,6 +438,96 @@ let test_initial_state_hash_arith_pvm () =
       Sc_rollup.State_hash.pp
       hash
 
+let dummy_internal_transfer address =
+  let open Lwt_result_syntax in
+  let* ctxt =
+    let* block, _baker, _contract, _src2 = Contract_helpers.init () in
+    let+ incr = Incremental.begin_construction block in
+    Incremental.alpha_ctxt incr
+  in
+  let sender =
+    Contract_hash.of_b58check_exn "KT1BuEZtb68c1Q4yjtckcNjGELqWt56Xyesc"
+  in
+  let source =
+    WithExceptions.Result.get_ok
+      ~loc:__LOC__
+      (Signature.Public_key_hash.of_b58check
+         "tz1RjtZUVeLhADFHDL8UwDZA6vjWWhojpu5w")
+  in
+  let*? payload = Environment.wrap_tzresult (Script_string.of_string "foo") in
+  let* payload, _ctxt =
+    Script_ir_translator.unparse_data
+      ctxt
+      Script_ir_unparser.Optimized
+      String_t
+      payload
+    >|= Environment.wrap_tzresult
+  in
+  let transfer =
+    Sc_rollup_inbox_message_repr.Internal
+      (Transfer {payload; sender; source; destination = address})
+  in
+  let*? serialized_transfer =
+    Environment.wrap_tzresult (Sc_rollup_inbox_message_repr.serialize transfer)
+  in
+  return serialized_transfer
+
+let test_filter_internal_message () =
+  let open Sc_rollup_PVM_sig in
+  let open Lwt_result_syntax in
+  boot "" @@ fun _ctxt state ->
+  let address = Sc_rollup_repr.Address.zero in
+  let metadata =
+    Sc_rollup_metadata_repr.{address; origination_level = Raw_level_repr.root}
+  in
+  let input = Reveal (Metadata metadata) in
+  let*! state = set_input input state in
+
+  (* We will set an input where the destination is the same as the one given
+     in the static metadata. The pvm should process the input. *)
+  let* () =
+    let* internal_transfer = dummy_internal_transfer address in
+    let input =
+      Inbox_message
+        {
+          inbox_level = Raw_level_repr.root;
+          message_counter = Z.zero;
+          payload = internal_transfer;
+        }
+    in
+    let*! state = set_input input state in
+    let*! input_state = is_input_state state in
+    match input_state with
+    | No_input_required -> return ()
+    | _ -> failwith "The arith pvm should be processing the internal transfer"
+  in
+
+  (* We will set an input where the destination is *not* the same as the
+     one given in the static metadata. The pvm should ignore the input. *)
+  let* () =
+    let dummy_address =
+      Sc_rollup_repr.Address.of_b58check_exn
+        "scr1HLXM32GacPNDrhHDLAssZG88eWqCUbyLF"
+    in
+    let* internal_transfer = dummy_internal_transfer dummy_address in
+    let input =
+      Inbox_message
+        {
+          inbox_level = Raw_level_repr.root;
+          message_counter = Z.zero;
+          payload = internal_transfer;
+        }
+    in
+    let*! state = set_input input state in
+    let*! input_state = is_input_state state in
+    match input_state with
+    | No_input_required ->
+        failwith "The arith pvm should avoid ignored the internal transfer"
+    | _ -> return ()
+  in
+
+  return ()
+
 let tests =
   [
     Tztest.tztest "PreBoot" `Quick test_preboot;
@@ -453,4 +543,5 @@ let tests =
       "Initial state hash for Arith"
       `Quick
       test_initial_state_hash_arith_pvm;
+    Tztest.tztest "Filter internal message" `Quick test_filter_internal_message;
   ]
diff --git a/src/proto_alpha/lib_protocol/test/unit/test_sc_rollup_management_protocol.ml b/src/proto_alpha/lib_protocol/test/unit/test_sc_rollup_management_protocol.ml
index 0dc5595a78ca49bf9834eba97e7b6dde541b3113..2cc1a0fec3a763c93746754a44f4bf47b3404dd1 100644
--- a/src/proto_alpha/lib_protocol/test/unit/test_sc_rollup_management_protocol.ml
+++ b/src/proto_alpha/lib_protocol/test/unit/test_sc_rollup_management_protocol.ml
@@ -125,9 +125,9 @@ let test_encode_decode_internal_inbox_message_transfer () =
     ( Script_int.(abs @@ of_int 42),
       string_ticket "KT1ThEdxfUcWUwqsdergy3QnbCWGHSUHeHJq" "red" 1 )
   in
-  let* deposit, ctxt =
+  let* transfer, ctxt =
     wrap
-    @@ Sc_rollup_management_protocol.make_internal_deposit
+    @@ Sc_rollup_management_protocol.make_internal_transfer
          ctxt
          pair_nat_ticket_string_ty
          ~payload
@@ -135,14 +135,14 @@ let test_encode_decode_internal_inbox_message_transfer () =
          ~source
          ~destination
   in
-  let* () = check_encode_decode_inbox_message deposit in
+  let* () = check_encode_decode_inbox_message transfer in
   (* Check that the size of messages that can be encoded is bounded. *)
   let msg = String.make 4050 'c' in
   let*? payload = Environment.wrap_tzresult (Script_string.of_string msg) in
-  let* deposit, _ctxt =
+  let* transfer, _ctxt =
     let open Script_typed_ir in
     wrap
-    @@ Sc_rollup_management_protocol.make_internal_deposit
+    @@ Sc_rollup_management_protocol.make_internal_transfer
          ctxt
          String_t
          ~payload
@@ -150,7 +150,7 @@ let test_encode_decode_internal_inbox_message_transfer () =
          ~source
          ~destination
   in
-  let*! res = check_encode_decode_inbox_message deposit in
+  let*! res = check_encode_decode_inbox_message transfer in
   assert_encoding_failure ~loc:__LOC__ res
 
 let test_encode_decode_internal_inbox_message_sol () =