Before attempting all this you should familiarize yourself with the Wiki :: zmprov command as most of the work will need to be performed from the command line. First of all you will need to create the mailboxes on your Zimbra server using Code:
su - zimbra
zmprov ca {name@domain.com} "" displayName "Test Account" That would create a user with the email address name@domain.com and a blank password. You could then use Code:
zmprov ma user@domain.com userPassword '{crypt}$1$dblahblahstuff....' To use the encrypted password from /etc/shadow and update their account with the same one.