I just found out how you can accomplish this.

You log in to PHPMyadmin with the database user that is used for the Digital Signage Press website.
There you go to wp_ds_program, and there you see all the playlists that are currently available.

If you have created the playlist for user/customer “All”, the you see “customerID” -1.
Every new user is created ongoing; 1, 2, 3, etcetera.

If you need to find out which ID the customer has, create a blank playlist as the new customer, and check the database like described above.
Then change the customerID to that number, and Voila, it has been moved.