Exim 3.35-1, considering special email-addresses as local/ How?

Hello NG,

At our company, we have an internal local mail-server running Exim on a
Debian stable, so employees can send themselves emails not going over
the internet, while all other mail is sent to our providers mail-relay
(we have a dialup connection). Incoming mail is fetched by fetchmail
from the appropriate pop-servers. Right now the situation is, that, to
send mail to a local user, we address it to
unix-username@local-fakedomain what works very well, but we'd like to
use our "real" email-addresses for sending mail. Unfortunately we can't
consider our real mail-domain as a local domain, because we have some
employees working from outside the building and not being able to access
our local server (dialup-connection), so my question is, is there a way
to tell exim to map a special email-address to a local unix user?

I've googled already but didn't find anything useful, /etc/aliases and
/etc/email-addresses also seemed not to be what I'm looking for
(email-addresses does it only the other way around -> mapping local
users to a email-address).

TIA

David.