To transfer your progress to another Android/iOS device:
- Make sure that your in-game profile is connected to your Google Play or Game Center account
- After that, enter the game with the same Google Play or Game Center account on your other device
- If, after starting the game, you aren’t offered to restore saved progress, go into the in-game settings and tap "Connect"
Note that you can't transfer progress from Android to iOS and vice versa.