diff --git a/skore/src/skore/sklearn/_estimator/feature_importance_accessor.py b/skore/src/skore/sklearn/_estimator/feature_importance_accessor.py
index f3ec08b3a..8fcb34f06 100644
--- a/skore/src/skore/sklearn/_estimator/feature_importance_accessor.py
+++ b/skore/src/skore/sklearn/_estimator/feature_importance_accessor.py
@@ -233,6 +233,8 @@ def _feature_permutation(
 
             if callable(scoring) or isinstance(scoring, (list, dict)):
                 cache_key_parts.append(joblib.hash(scoring))
+            else:
+                cache_key_parts.append(scoring)
 
             # order arguments by key to ensure cache works
             # n_jobs variable should not be in the cache