It's going well! I must say, to my considerable surprise and rather great relief. I migrated some sites in the transition from Drupal 7 to Drupal 8 and that was a migraine experience. Now it's going perfectly. Saved and downloaded the database from the source site. Then uploaded that database dump to the new server. To be precise: on the new VPS, I gave the command within MySQL to import a database dump. Whizz... done! Yes, then you're not there yet... So I went over it a few times until I got the right order:

1. define a new site by linking the IP address of the VPS to a "name" of a subdomain in my own hosts file. This can be done without any problems, even if the domain has not yet been transferred.
2. On the document root defined in apache on the VPS, create a symbolic link to the directory where Drupal 8 is installed.
3. Under Drupal 8, create a new directory within the sites folder with the name of the desired site as filename.
4. Create a database for the new site in MySQL on the VPS.
5. Call up the new site in your browser. You should now end up in the Drupal 8 installation procedure. Follow that procedure until there is a running site. This way the settings.php file of the new site will be filled correctly.
6. Upload the database dump from the old site to MySQL on the VPS.
7. Copy the contents of the old site's files directory to the new site's equivalent directory.
8. Reload the new site in your browser. It may all look black and white. Then we have to fiddle a bit. Reload the theme setting. The theme may need to be activated first. Save the desired settings.

Nine times out of ten you're done! You may still need to tweak a few things here and there, but I didn't run into any major problems, as long as you make sure all files on the new site have the correct user and group, otherwise you'll get all kinds of error messages.
In any case, I managed to migrate the site of Anja's practice in this way without any problem.