It looks more like the SMTP service needs to be configured to "Relay" email... Usually this involves telling it what YOUR mail domain is, and then any mail destin for a domain other than it's own will cause it to go out to the world, and try to relay the message to the real server.
But, be careful! This is how spammers exploit email servers. They look for SMTP listeners that will relay for them. You want to make sure yours will only accept relay mail from "localhost", or whatever machine will be connecting to it to do the sending.
A more secure way is to block port 25 inbound at your firewall to this box, so this SMTP server is not visible to the outside world.