Outlook 2013 provides support for this out of the box.
When you are connecting to Exchange 2010 SP2 RU4 or later, then you can also configure this in OWA.
A copy of the sent mail will also reside in the Sent Items folder of the member’s personal mailbox.
Note: If the user has used the Outlook 2013 feature to change the folder that Sent Items are saved to, the messages will be copied to that folder instead of the user’s Sent Items folder.
For Outlook 2003, Outlook 2007 and Outlook 2010, you’ll need to install a Hotfix or the latest updates to control the Sent Items for Delegate mailboxes via the Registry.Both these issues have been corrected with i Tunes version 10.1.0.56.