I found a different solution in collaboration with the plesk-premium-support:
1.
The Plesk Migrator program is the recommended way to migrate.
For source servers without Plesk (custom hosting / non-Plesk system) such a migration is only on the command line and you would have to manually create a hosting description file for the migration.
The installation, configuration, and execution procedures are explained in more detail in the following Knowledge Base article:
How to migrate from a Linux server with custom hosting to Plesk?
It also refers to the relevant parts of the documentation Migrating from Custom Hosting.
2.
Often the Maildir structure is used on the source and the destination server, it is possible to simply copy the mails from the file system to the other server. To do this, however, the domain (s) and mailboxes must first have been manually created on the Plesk Onyx server.
3.
A feature to migrate mailboxes directly from a server without Plesk to Plesk Onyx does not exist.
You should be able to migrate using the third-party programs IMAPSync and the RCimapSync you mentioned.
Thanks for your reply.