The most common casualty.
THE USUAL CAUSES
MX records not recreated at the new provider The mail hostname not resolving cPanel email routing set wrongly Accounts not recreated
CHECKING MX RECORDS
Look up your domain's MX records. Are they present and correct?
CHECKING THE HOSTNAME
MX records point at a hostname. That hostname needs an A record.
THE ROUTING SETTING
If mail is hosted elsewhere, cPanel email routing must be set to remote.
If it stays local, mail sent from your website to your own domain is delivered to a local mailbox and appears to vanish.
That is the failure people cannot explain.
IF MESSAGES ARE MISSING
Messages delivered to the old server during propagation are still there.
Check the old mailbox before cancelling.
IF OUTGOING MAIL GOES TO SPAM
SPF and DKIM need setting up here. Check cPanel Email Deliverability.
WHAT TO TEST
Send and receive, both directions, from each account.