In order to transfer your installation from one machine to another, simply uninstall the application from the original computer. This will release the license key so that you can reinstall it on a different computer, using the same license key. A single key can only register a single computer at a time.
Please note that the license keys are Mac or Windows-specific and can not be changed.
If you need to look up your license, simply enter the email that you used to purchase into the Lookup tool linked below. Alternatively, you can search your email for the original key that would have been sent from firstname.lastname@example.org