1. Create a secondary MX record pointing to the new static IP address
(Once this transfer is completed, the server will no longer be responding at the old mx record address, and mail will begin being delivered to the secondary MX record by default)
2. Change the current DNS A record of mail.yourdomain.com to the new IP address. (DNS Propogation takes approximately 4-48 hours on average within the US)
This should make the transition nice and smooth for you. The default installation for almost all network servers is to allow delivery up to 48 hours before the sending server returns a non-delivery report to the sender. Your transition and DNS record propogation should not take 48 hours. This way the server is offline/unavailable and the sending server will try to send again repeatedly over 48 hours until the message is delivered successfully. This is handled by mail servers on a per message basis, so you shouldnt have any problems at all. You also have the advantage of the weekend for DNS propogation. Statistically less legit emails are sent and received over weekends so you run very little risk of actually losing legit messages.
