Copy the mailboxes. Cut MX only after one account receives.
imapsync onto the new Dovecot, PTR requested on the new IP, SPF updated. The old server stays up. Outlook profiles are not part of the job.
Mailboxes, a test, then DNS
IMAP to IMAP while the old MX still receives. A final pass in the window. Maildir size decides the time, not the number of domains on the panel.
One account logs in on the new IP, sends, and the message is accepted. Webmail is enough. We do not cut MX on a server that has not received a message.
TTL already low. MX, SPF, DKIM selector, PTR. The old box keeps port 25 open for a day so a late delivery is not lost.
This is the mail move. The VPS move is the other page.
Mail can leave a server that still hosts the sites. The reverse is also true. Doing both in one window is a server migration, quoted as that.
Quoted from the mailbox count and the Maildir size
A handful of mailboxes is a small quote. Years of mail for a company is not an hourly surprise. Discovery is €55/hour if we cannot see the server yet. Zero downtime is not promised.
Moving mail, and the sites can stay?
Tell us the mailbox count and both providers. No mailbox password in the first message.