email and domain issue

[tlkhorses]

It appears I have an issue with outgoing email setting in customers who have a domain on our mail server. Our company domain is companydomain.com. The customer has a domain of customerdomain.com. Setting their email client (outlook) with incoming mail server as mail.companydomain.com and outgoing mail server mail.companydomain.com, their email will work. Changing the outgoing mail server to mail.customerdomain.com does not work. There is an A record for mail.customerdomain.com with the public IP of the mail server in their domain, dns settings.

So my question is why doesn't mail.customerdomain.com work for the outgoing mail server?

tk