Restore Things to iPhone from iTunes

Solution 1:

If you're absolutely sure that you have SYnced the phone and the app is still not there, you can try to remove it from iTunes too. Then you go to the App Store (make sure you are logged with the SAME account you were when you bought it for the first time) and buy it again, the store will inform you that it's "a free upgrade" and will re-download it. It will not charge you again.

Solution 2:

Make sure it is selected as an application that syncs to the iPhone. If it is visible in iTunes then it should still be able to be synced. If that doesn't work then open up the app store on the iphone and install it from there. You won't be charged as you have already purchased it.