Download and install the plugin as a trial on the new computer. Do NOT choose "Have License". The trial is fully functional for 30 days.
Once installed go to licensing and note the serial number.
Go to the old computer where the plugin was installed and note the serial number.
Once noted send an e-mail to email@example.com and tell us which serial number you'd like to cancel and which you'd like to make active.
Be sure the computer has internet access and you are in the "Online" tab in the License window.
The licenses will automatically be updated as soon as it's configured in our system and you've quit and relaunched Photoshop.