For DSM 2.0/2.1 users:
Please contact the support desk at email@example.com to log a ticket with your request and the last 10 characters of your unique license key.
The licence will then be reset by one of your support personnel, allowing you to setup the add-on module on a new computer.
For users of DSM 4.0 and newer versions:
Head into File->DesignSpark Options->Licence and click on Deactivate licence. Make sure you are online. This will reset the key for a new activation.
The re-install steps will be the same as in your licence e-mail. Or, you can follow this tutorial from step 4: https://designspark.zendesk.com/hc/en-us/articles/212216845