Go to "User CP(top left on the site)", in the tab "Settings & Options" on the left side you'll see "Edit Options", click on it, scroll down a bit until you see "Private Messaging" and check the box at
"When sending private messages the forum can make a copy of the message in your Sent Items folder.
Save a copy of sent messages in my Sent Items folder by default"
After that just scroll down and save the changes. You'll see your sent private messages now in the "Sent Items" folder.