First we list every address in use today, including the ones printed on invoices and vehicle stickers, so nothing is switched off by accident. Then we create the new mailboxes and copy the old mail into them while the old system still runs.
Only then do we change the MX records, add SPF, DKIM and DMARC, and set forwarding from the old addresses for a transition period. Phones and laptops are configured in the same visit, and every user gets their password reset and two-step verification enabled.
We close with a written handover: the admin login, the DNS records as they now stand, the mailbox list and the licence renewal date. Anything that needs changing later takes one WhatsApp message.