The PM moves to your sent box once the PM has been read. Which means, the user may have had the pop-up box, they may have gone to their inbox, but haven't opened the PM. Once the PM has been clicked on, it will move from your outbox to your sent-box.
On another note, if you receieve an email saying you have a new private message, then you go to your inbox and there is nothing there, this is caused by the fact the the person that sent the PM has deleted it from their outbox!
oh, and another sub note...if a PM is in your outbox, you can still edit that PM before the user gets it