How to transfer Filmage Screen Pro to a new device?

As for Filmage Screen.dmg:

If you want to unbind your license code to one device and link it to another, please contact support@filmagepro.com to claim your request with your license code and email address. We will unbind it for you.

As for Filmage Screen Pro (Apple Store):

Download Filmage Screen Pro from Apple Store with the same Apple ID in your new device and open it. You don't need to pay for a second time.