Ah, I see
So on the network edition, you can backup all the mailboxes.
I did miss the first time that you are on the network edition.
General info is here:
Network Edition Backup Procedure - ZimbraWiki
Some considerations should be
1) DNS-make sure that mx records get transferred to the new box.
2) Move over (once you've backed up) the entire /opt/zimbra/backups, if that's where you backed up. If not, move your other location
3) make sure the files are Zimbra user accessable.
and if something goes wrong, let us know
john