The key is registered to phone serial number and If it`s the same iphone (just restored with iTunes) the serial number will be the same and the activation key will work but if you have a new iphone the old key will not work because it is a different serial number.

The migration is free for devices change into the period of 1 year starting from the paypal transaction ID. After this one year period we grant a 50% off discount to active a new device.