To transfer your game progress, you need to log in on your new device to Google Play Market/Amazon Store with the same Google/Amazon 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
3) choose the option Connect 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 Puzzle shop, the My Packs category: https://androidpuzzlessupport.zendesk.com/hc/en-us/articles/360035874851-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.