@matteoca it should be automatic providing you are using the same google account on the new device. However, Google Play can sometimes be a little finicky at letting the apps know when this has happened. If you go through the purchase flow for a lifetime subscription again it will say "You already own this item" and it will kick it back into working.
Hope this helps, if not please drop an email to android@stealthcopter.com and I'll sort it out for you!
