Below is how I have migrated mail server with minimum downtime and routing mail to the new server via mailertable, if IP is still pointing to the old server and has not resolved for some ISPs.
48 hours prior to migration, set the TTL value for the mail server DNS A record to a short time like 15 minutes.
Prepare for the migration, rsycing the mail spool folder and the user home mail folders.
rsync --progress -a -e "ssh -i /root/.ssh/key -p 22" old.mailserver:/var/spool/mail/ /var/spool/mail/
rsync --progress -a -e "ssh -i /root/.ssh/key -p 22" old.mailserver:/var/www/web1/mail/ /var/www/web1/mail/
rsync --progress -a -e "ssh -i /root/.ssh/key -p 22" --exclude='*/bak' --exclude='*/web' old.mailserver:/var/www/web1/user/ /var/www/web1/user/
Run rsync the final time.
Setup Sendmail with mailertable to relay mail coming in to the old server over to the new mail server. This is a similar setup for secondary mail servers.
Add "FEATURE(`mailertable', `hash -o /etc/mail/mailertable.db')dnl" to "/etc/mail/sendmail.mc" if it does not already exist.
Create "/etc/mail/mailertable" file with contents of the routing table:
The square brackets skips checking MX records, so IP can be used instead. Remove domain name from "/etc/mail/local-host-names" so mails do not get delivered locally.
Edit "/etc/mail/access" to relay mail for the domain.
makemap hash access.db < access
makemap hash mailertable.db < mailertable
Test by telneting to port 25 on the old servers' IP and sending email. This should get relayed over to the new server.
Use a new subdomain and redirect existing webmail url to the new server.