How do I move users mailboxes to a new server

I have a dedicated Matrix server with user accounts on that I want to move to my new dedicated server. Some Users access their email by webmail so how can I get to their pop3 mailboxes and move them accross to new accounts created on the new server. The domain will stay the same and I will move the DNS and MX records once I know how to transfer the users mailboxes. Both servers are running redhat linux.

mailboxes are created via user accts, and through my own
experience with server moves, I know that you cannot move
user accounts. Unfortunately they'll have to be recreated
on the new server.

Of course you can copy over the site data, databases, etc.