Note: Some Android phones have an option to migrate existing data to your new phone. In that case, you might find that Lemmings has already been automatically downloaded, and your progress has been shifted over to the new device.

If your progress has not been shifted over automatically, you can follow the below steps:

1. You must have already played the game and made some progress to shift over a save. While playing the game, you will get a "Save your progress" pop-up, which tells you to log in to GooglePlay Games. If you have not received this pop-up, you can also do this manually by going to your settings and tapping Log in to GooglePlayGames.

2. Log in to GooglePlayGames to save your progress. If there is no GooglePlayGames profile yet, your phone will guide you through making one on the spot.

3. Download Lemmings from the Play Store on your new phone.

4. Play through the four tutorial levels.

5. Once finished, go to the Settings menu and select "Sign in to Google Play" at the bottom.

6. The game will now present you with the choice to import your GooglePlayGames save file or keep your local save - Details are provided for both options.

7. If you pick the GooglePlayGames save file, this save will now be imported and you can resume playing Lemmings from where you originally left off on the old device.