Very easy...
under thunderbird, create an imap account that lead to your user's zimbra account. Then your user just have to drag/drop e-mails from local account (old pop) to zimbra imap account.
Caution for the zimbra login name under thunderbird, put /tb at the end to avoid some date/time issue with e-mails.
For example use
toto.tit@domain.com/tb as login name
You will have some difficulties to migrate address books an especially mailing lists, look in forum to get some tips for this