How do I transfer my game progress to a new device (same platform)?

To transfer your game progress, you need to log in on your new device to the Microsoft Store with the same Microsoft account you used on your old device.

Also, please, log in to Magic Puzzles on your new device with the same Facebook account you used for registration in the app on your old device:
1) press the Settings icon in the upper right corner

 2) My Account

3) choose the option to Log in with your Facebook account and Live ID (to restore purchases made with real money) and enter your details

After that, your coins and level will appear on the new device.

Puzzle packs can be restored to the My Collection page from the Jigsaws Store, the My Packs category: https://win8puzzlessupport.zendesk.com/hc/en-us/articles/360036041212-How-do-I-restore-my-puzzle-packs-

Unfortunately, created from your own photos, started, and downloaded from the Club puzzles do not sync between devices.