How to migrate a mail server without downtime?

Question

Exim

Good afternoon everyone!
I plan to move the mail server from one physical server to another. On both ISPManager servers (respectively exim+dovecot). There are no problems with copying data itself. But I can't figure out how to switch the server? If I rewrite the record in DNS, then while it will disperse, time will pass. And letters during this time will come to the old server, which will be physically turned on and working (because other mail domains remain on it). Only proxying from the old server to the new one comes to mind (using Exim?).
Who had experience - tell me.

Answer 1

Proxying is the best option, as long as not the entire server is moving, but some of the boxes. You will have to proxy for at least 2xTTL DNS records.

Answer 2

https://debian.pro/1139
And the rest you are right.