I do not see a Sent Messages section in the Private Messages area. This, I think, would be a fairly simple and convenient implementation. (Unless, of course, I'm completely missing something)
Go to your "List Messages" and then at the top of the page in folder control you can see "Jump to Folder." Normally it says Inbox but it has a drop down icon and underneath this is Sent Messages.
Also, in your User Control Panel (UserCP), Edit Options page, make sure Save a copy of sent messages in my Sent Items folder by default is checked.
