You should see if Eudora can do this for you. Many email clients have the capability of filtering incoming mail and applying rules. Usually one fo the rules that can be applied is to forward the email.
I believe that Eudora hasn't been supported/updated in a while (though I could be wrong about that), but I'd think that it would support this type of feature, though you might need a 'Pro' version. Eudora used to have a free version that had some features removed compared to a paid-for version. I don't know if that's still the case or what version you might have, but it would probably pay to make sure that the client you're using doesn't already support what you need.