No, license keys are single activation keys that lock to the hardware/software combination and cannot be moved to another system. If this action has already occurred and your license key is now not working anymore, then your only recourse is to contact us for a license key reissue, assuming that your license key is valid and not expired. We can then provide you with a new key that you can use to use your license again.
We would like to point out however that if you are deploying your system on Amazon AWS and you are looking to use autoscaling or you wish to rebuild your instance regularly for security regulatory purposes, then you can instead make use of the Amazon tiered instances on the Amazon Marketplace. These are launched through Amazon's systems and are billed directly through Amazon's systems as well, and these can be moved, copied, and reinstalled, just fine, as they will just pick up their licensed state from Amazon's systems and you will be billed for each instance that you actively have running.