You can restore or transfer progress to another device yourself as follows:
1. Link your progress to your Google Play Games profile: Open the "Settings" menu in the game (the gear icon) and click the "Link account with Google Play" button. The game will prompt you to enter your Google Play profile e-mail and password or select the desired account.
2. Go to Google Play Games on the desired device under the same account and download the available profile from the cloud.

You can also synchronize your progress in another way: You just need to link your game accounts on different devices to one Facebook account. This method will allow you to further sync your progress with other platforms such as Windows Store, Amazon Store and Galaxy Store.
First, you need to link your main game to your Facebook account. After that, link the game on the other device to the same account, and your progress on the two devices will be synchronized.