Synonyms cannot be added to a folder in Favorites when running a search on the "Object Search" screen because the "Add the selected objects to the Schema Browser favorites list" is not enabled when Synonyms are selected.
This works when Synonyms are selected alongside other database objects but when you click the "Add the selected objects to the Schema Browser favorites list" button to add the objects to Favorites, all objects are added except Synonyms.
Group Favorite Objects
You can group objects that you use frequently into a tab on the Schema Browser. These different objects can be grouped into one or several folders. Folders are specific to an instance (not a connection or a schema).
Objects supported in this window include: tables, views, PL/SQL code (procedures, functions, packages, triggers), and files.
Waiting for fix in a future release of Toad for Oracle.