Iphone problem question

So a friend of mine apparently never thought it relavent to link the information in pokemon go and Fire emblem heroes to his nintendo account, and sure enough his phone is now not able to hold a charge and thus cannot turn on at all to get it linked.

He mentioned a warranty and that he'd be getting a new one for five dollars, does anyone know if the data on his phone will be transferred over? He's pretty bummed out about losing his progress on both, so I figured I'd ask if anyone knows if there is a fix/if it just wont be a problem.