Game save data between IOS accounts?

My wife has been playing Sims 4 for several years on an iPad we share that is logged into my Game Center account. She wants to move her game to an iPhone.

I created her an EA account and used that account to link to the IOS game. I backed up the game after that. If I install Sims on her new phone will that save data transfer if I log into the EA account on that phone as well?

It seems you cannot unlink the Game Center account from the phone and I am hesitant to do it from EA. She has spent a lot of time and money over the last 3 years building out her game. Any help would be greatly appreciated!