I have a similar problem.
I set up the email system in AbanteCart with the default on the screen "MAIL". Is there anything else I need to set?
I have set up a webmail account in connection with this shopping domain "admin@somedomainname.com"
Abantecart is installed in "somedomainname.com"
I also verified that the webmail.somedomainname.com works already.
In my case, I am using Hostgator