When sending mail as another mailbox/e-mail that was added to your Outlook the sent item does not end up in the other mailbox, but in your mailbox.
MSExchange.org - Outlook, Delegated Access and the infamous "Sent Items" folder behavior
MSOutlook.info - Save Sent Items in owner’s mailbox
Microsoft Support - An e-mail message does not appear in a user's mailbox if the e-mail message was sent on behalf of the user by a delegate in Outlook 2003
Microsoft Support - When you send an e-mail message from a shared mailbox in Outlook 2007, the sent message is not saved in the Sent Items folder of the shared mailbox mentions the DelegateSentItemsStyle DWORD registry key for Outlook (which only works consistently when Outlook is configured in cached-mode, see Microsoft Support - Email remains in the Outbox when you use the DelegateSentItemsStyle registry value).
Microsoft Support - Email that you send on behalf of someone is not saved in their Sent Items folder mentions that the DelegateSentItemsStyle registry key is not available in Outlook 2010 RTM without a patch).
Microsoft Support - Messages that are sent by using the "Send As" and "Send on behalf" permissions are copied only to the Sent Items folder of the sender in an Exchange Server 2010 environment mentions the *-MailboxSentItemsConfiguration PowerShell cmdlets (not (yet) available in Exchange Server 2013).