Minecraft data from iphone - how to back it up?

My son has hours and hours of time put into building his "world" on Minecraft, using his iphone.

Now he will be going to a new iPhone.

How do I get the data for his "worlds" backed up, so that it can be transferred to his new phone, i.e. so he does not lose the work he has put in building his world?

Ideally, there would be some way for Minecraft to be backed up in the cloud, so that when the new phone is activated the data will appear on it without having to do anything (other than restoring the new phone)

If not, then can I back up his old phone to iTunes?

And if not that, is there some other, more painful but still viable way to get it done?

Thanks