Some server administrators prefer that all outbound email be handled by an external server or a third-party service. If you would like all email routed through another server, you can setup your server to use a "Smarthost."
If you were okay with using a server-wide smarthost what you can do is go to WHM's [Home »Service Configuration »Exim Configuration Manager] and then search for the option "Smarhost Support."
Then you can enter an asterisk (*) and a space, followed by the value for the smarthost based on the server. For example, if you knew the IP of the sending server you could use:
Or if you knew the hostname of the server you could use:
More information on this can be found here.