diff --git a/.gitlab/container_build/docker_linux.yml b/.gitlab/container_build/docker_linux.yml
index a6ee15173c653..a5ae000a54e18 100644
--- a/.gitlab/container_build/docker_linux.yml
+++ b/.gitlab/container_build/docker_linux.yml
@@ -271,7 +271,7 @@ docker_build_cws_instrumentation_amd64:
     IMAGE: registry.ddbuild.io/ci/datadog-agent/cws-instrumentation
     BUILD_CONTEXT: Dockerfiles/cws-instrumentation
   before_script:
-    - cp $CWS_INSTRUMENTATION_BINARIES_DIR/cws-instrumentation.amd64 $BUILD_CONTEXT/
+    - cp $CWS_INSTRUMENTATION_BINARIES_DIR/cws-instrumentation.${ARCH} $BUILD_CONTEXT/
 
 docker_build_cws_instrumentation_arm64:
   extends: [.docker_build_job_definition_arm64]
@@ -283,7 +283,7 @@ docker_build_cws_instrumentation_arm64:
     IMAGE: registry.ddbuild.io/ci/datadog-agent/cws-instrumentation
     BUILD_CONTEXT: Dockerfiles/cws-instrumentation
   before_script:
-    - cp $CWS_INSTRUMENTATION_BINARIES_DIR/cws-instrumentation.arm64 $BUILD_CONTEXT/
+    - cp $CWS_INSTRUMENTATION_BINARIES_DIR/cws-instrumentation.${ARCH} $BUILD_CONTEXT/
 
 # build the dogstatsd image
 docker_build_dogstatsd_amd64: