a real user on your system? If that is true you could create a .forward file in the user's home directory. Check that the "userforward:" part of exim.conf is correct as well.
A very simple solution but it should work.
If this applies to all users at some domain, read up on the Exim FAQ over at exim.org. Here's a snippet:
Q0316: I would like to forward all incoming email for a particular domain to another host via SMTP. Whereabouts would I configure that?
A0316: Use this as your first router:
driver = manualroute
transport = remote_smtp
route_list = the.particular.domain the.other.host
You will also need to adjust the ACL for incoming SMTP so that this domain is accepted for relaying. If you are using the default configuration, there is a domain list called relay_domains that is set up for this.