You could try syncing and then backing up your old phone to your computer with iTunes and a cable connection (don't use the useless iCloud!) then restore the new phone with the back up you've made of the old one.
I went into panic mode when I did this this with my iPad and DH2014 wasn't on there afterwards, but you just find the apps tab in iTunes and click install and it puts it back with all the game data intact.
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I went into panic mode when I did this this with my iPad and DH2014 wasn't on there afterwards, but you just find the apps tab in iTunes and click install and it puts it back with all the game data intact.