Hi Gregor!
To do what you ask (i.e. migrate new mails that could arrive on the old server/account after the initial migration), I suggest doing this from the beginning:
1 - use the "MAilbox Migration" tool ONLY AND EXCLUSIVELY to migrate Calendars/Contacts/Tasks/Notes (you do NOT have to migrate the mails!!!!)
2 - use the "Email Retrieval" tool to migrate the mails (possibly DO NOT use POP3, but instead IMAP or the specific tool for the server to migrate), setting the "Retrieval Method" to "Automatic"
Gabriele Maoret - Head of SysAdmins at SERSIS
Currently manages 6 SmarterMail installations (1 in the cloud for SERSIS which provides services to a few hundred third-party email domains + 5 on-premise for customers who prefer to have their mail server in-house)