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?
I am unsure if this would answer your query. Create a rule on OWA (webmail) and open your shared mailbox on which the sent item has to be saved. Open Options in the (Shared Mailbox webmail)
And go to Mail -> Automatic processing -> Inbox and sweep rules and create a rule to download the Sent Items which are saved in Personal mailbox
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