Given your server is properly setup (you run Exim) but you or your customer can not send out email with a bounced error:
user@domain.com is undeliverable: The mail server could not deliver mail to user@domain.com. The account or domain may not exist, they may be blacklisted, or missing the proper dns entries.
The problem is because the other end has MX set to an IP. Exim software will not recognize as a proper MX hostname and won’t be able to deliver.
You would ask the other end to set a CNAME for the IP => then set MX to that CNAME.
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Thank you VERY much for getting rid of my headache