Jigsaw Puzzle Pro and Jigsaw Puzzle Free are 2 separate applications in the iTunes App Store. Apple also treats these as 2 separate apps and does not allow the purchases to be transferred between the 2 separate apps. Purchases on Jigsaw Pro can only be restored in Jigsaw Pro and purchases made in Jigsaw Free can only be restored in Jigsaw Free.

If you want to have the same features as the Pro version but still keep your purchased puzzles, you just need to "Upgrade". The Premium Upgrade allows all the same features as the Pro version of the game.The Pro is simply offered for those users who want that experience from the get-go.