[exim] Newbie to exim4

Hi All

Please excuse me if this is not the correct way to ask these type's
of questions in the mailing list.

Where do I start?

We have a mail server at another provider and mail is working fine,
but the problem is that we are sitting at our office sending mail to
each other, but the mail goes all the way out to the mail server,
and we have to all fetch it through the internet to our MUA's.

I have installed exim4 at our office on a Debian Sarge 3.1 box
and I want it to be able to do the following:

1.) External mail server has several accounts, some of them at the
office
and some not, i want local users at the office to be able to send mail
to this
server ( at the same domain) and be delivered to their mailboxes for
this
domain (Which works if I edit /etc/exim4/update-exim4.conf.conf and
add the domain in dc_other_hostnames='example.com'

The problem comes in when users at the office wants to send mail to this
domain to a users that is not on the box and exim rejects it with
"Unrouteable address"

2.) What routers rule do I put in place to send mail for valid users on
the box
directly to them, and for all other "unknown users@???" to the
listed
MX via the smarthost?

What other information can I provide for assistance, please?

Thank you.

Regards
Jono