1. On a single ServerDirector, create two name based VDSes.
2. Use a third party SMTP server to send mail from firstname.lastname@example.org to a user at email@example.com.
The problem occurs because some customers are forced by their ISP to use their ISP's SMTP server, instead of their own SMTP server on the VDS.
In order to support this configuration, the VDS owner (a.com) should clear the "Outgoing mail server" field in the "Email FTP --> Settings" tab.
The property "Outgoing mail server" is in the VDS level which means that all the user accounts of the VDS are effected.
In case that "Outgoing mail server" was modified to false, any VDS's user that need to send an email
to user of a name based VDS on the same ServerDirector, must use their ISP's SMTP server.