My son broke his iPhone 4 screen and we are getting him a new one. He has a lot built in Minecraft PE. Is it possible to move all his worlds to the new device and how would you do that?
The game data is stored on your device. You will need a program that allows you to access this data. I can not recommend any such software personally, however once you have this the game data can be found
You should be able to use the same software to download the necessary files, and then transfer them to your new phone.
You should also be able to use iTunes to back up your old phone, and then restore it to a new phone, even if they have different basebands but provided they are compatible.
As a side note, if you just want to keep your phone, its easy to have the screens fixed/replace nowadays. And generally a cheaper option if your device is not under warranty.
This question has been asked and answered before, but I could not find the previous question thread, so I went ahead and answered it again. If you find the thread please don't downvote me, I searched for it, and even checked my history as I was the one who answered it before as well.