Hi Klaus,

First you deactivate the license on the old computer and then download and activate the license on the new one, the videos for activating and deactivating are below, in case you need the steps on how to do that:

www.youtube.com/playlist

The installers are in your RWS account - Downloads and the activation code is on the Licenses tab. You can check there if the license deactivated, it would show In Use if it was not. 

Since you have the Plus edition, you should see if both activations are in use or not. If both are in use, you can reset them - Reset license button.

If you encounter any difficulties, you can raise a support ticket yourself from your RWS Account - Support tab, since you have an active support contract.

Please let me know if you have other questions.

Kind regards,

Anca