Hi Markus,
I have two ideas about this. Which you could use depends on the way the migration is done.
1. Migrate workflows with an action
There's one workflow action which has an "overwrite author" option. It's on the second tab I think of the start workflow (sql). I currently don't have access, so I can't look.
2. Use REST with impersonation
If you migrate the data using REST API you could use the impersonation property when you fetch the access token. This way you could do the migration directly in the name of the user. In this case the users need to have the appropriate permissions.
Remark:
Make sure that the old users are still active in AD. If they are not, add an external user with the correct BPS ID for the deactivated user. Otherwise you will run into problems, at least with the second approach. :)
Best regards,
Daniel