If when you send mails in Outlook for Mac 2011 and the sent email messages move to your Outbox folder but never move to your Sent Items folder, then this article may interest you.
To resolve this issue, Microsoft KB2434474 recommends you try the following steps in no particular order:
1. Make sure Outlook is not offline
2. Empty the Outlook send folder
3. Use the Shift key and restart Outlook