Yes it is very possible
You do need to connect your game to an Originaccount.
Once you have the account you can play your game on any device that holds TSTO by loggin in.
When you first download the game on a new device it will take you to a default Anonymous town. You do not have to play that game if you dont want a second town. To find your old game, find the Login button. Login buttons: Welcomescreen, bottom left. Friendscreen (minitowns) tap Handshake, bottom right in the pop-up "add origin friends" enter log in info.
Either exit the game to access the Welcomescreen or play through the first levels to access the Bart/Milhouse button to take you to the Friendscreen with the minitown.
It may say "your other device did not save" ignore it and Play Now/Continue. The loss if any is minimal. Only your last session so you might have to reset tasks or start a build again but nothing further back.
Good luck!
To create an Originaccount.Bart/Milhouse. Friendscreen (minitowns): handshake icon. Popup: bottom right: login. Use the Sign Up button if you want to create an account.
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D'oh! - Em