A step forward with exim

[Vittorio <vdemart@supereva.it>]

At home I've set up a small network made of 1 server (debian 3.0 on an
old pentium notebook and adsl internet connection) and a couple of
PCs, one with linux debian and the other win 2000.

My final aim is to use exim on the server as an SMTP, i.e., to forward
mail from different users on my home network to the outside world
through my ISP SMTP server.

On the debian server I've build a very basic exim configuration
selecting option 2 from eximconfig, and, adding some entries to the
/etc/email-addresses.


Finally, now I'm able to send email through sendmail FROM THE SERVER
to the internet with exim correctly rewriting the "From:" address as
I've instructed it. 

But, I'm unable to send email from mozilla mailer in A CLIENT, where
I've setup the mailer for a known internal user (present also in
email-addresses on the server) and in the SMTP field I've put the name
of the SERVER computer. 

Bear in mind that during the configuration I've told exim to accept
post from my machines (listed their IPs).

Could someone straightforwardly tell me what are the necessasry steps
to make exim on a server work as an SMTP?

Thanks

Vittorio