Note that you'll need to connect your phone(s) to your PC and run a Chrome app (or desktop app) in order to enable the backup functionality. It's kinda weird that way. If you can make it through those hoops, Helium will back up pretty much any app/game and restore it to your new device.
There may be some other thread about Helium in the forum section.
One last thing though - I am not 100% certain that the achievements copy over. I know that on some of my older devices, I had things like rapid rank III unlocked but not on my newer devices.
Oh ... I see you also put it as an enhancement request and Andrew responded with much more detailed info than I did