Let's talk standard terms. To receive e-mail, you need an MTA (sendmail, Exim, Postfix, whatever). To read mail you need an IMAP/POP3 server. I don't know, how your groupware works, but common sense suggests it uses IMAP to acces your mail. If it does, just point it to your hosting server.
If on the other hand it requires you to give access to the mail servers database to create mailboxes, you're in for some pain.
In this case you first need to set up your shiny new mailserver with the groupware software. If you're done, you need to test it thoroughly. Finally, you need to switch your MX records and move your mailboxes' contents.