Hello-
The existing messages will not be forwarded.
I would say the easiest way to migrate the old messages is to enable Web Inbox and have the users download the messages. Web Inbox is enabled on the CoS level.
Navigate to: Class of Service > Class of Service > the CoS of the user (you could create a new one just for the users that require this)
Check the box for 'Allow Users to Use the Web Inbox and RSS Feeds'
The user should be able to login to https://<CUC- Server>/inbox/ using their username and password.
Thanks,
DJ