To route email for a specific domain to a remote server on WHM using Exim:
 
Go to Exim Advanced Config Editor and add the following under the PREROUTERS section
 
special:
driver = manualroute
transport = remote_smtp
route_list = domain1.com somesmtp.com; domain2.com somesmtp2.com
 
Where domain1.com is your domain and somesmtp.com is the address of the server to route mail for that domain to