E-mail sent from (not on behalf) a shared mailbox is stored in the user's mailbox sent items folder instead of the sent items folder in the shared mailbox.
There is apparantly a hotfix (KB2181579) but that only works with Cached Exchange Mode enabled.
Enabling Cached Exchange Mode is PITA, as it has its own problems (missing folders, calendar items missing/not synchronizing etc)
Is there a way to store the sent items in the shared mailbox, which does not involve rules?