Determined that the recipient wasn't receiving emails from the Accounting shared mailbox had an inbox rule that was moving those emails to an obscure folder. This was resolved by simply deleting the inbox rule on the server side. Then, explained to the user why the default behavior in Outlook is to place sent items from shared mailboxes into the user's own mailbox, though it actually sends from the shared mailbox. Offered to change the behavior if desired. Lastly, explained why the user can no longer access the Accounting shared mailbox directly via username and password - it's for security reasons.