[exim] Users wanting to send mail from a dial-up (ISP) conne…

Hi,

I'll try to keep this as short and clear as I can...

Simply put, I would like to know how to configure Exim (4.32) to allow a
user to send e-mail when he/she accesses by way of a dial-up connection
(e.g. from home), using e.g. Outlook Express.

How do I configure Exim to allow a user with an account on the mail server
( therefore a $local_part ) send out mail from his/her dial-up Internet
connection? Mail sent to another user locally works, but out-going mail
returns a message in the lines of: relaying not permitted from host
xxx.example.com (sorry I can't be more specific with the error message at
the moment). I have courierpop and courier-imap installed, and the user can
access his/her own mail, and the mail server is a Debian 3.0r2 Woody
installation.

I'm having a hard time understanding this because I thought Exim checks the
From/Sender e-mail address (which would be of course user@???) and
will then attempt to send the mail.(?)

Would I have to specifically allow Exim to relay from the ISP the user is
connecting from? If so, can you please explain why that is, and how I would
have to configure it.

All help with this will be greatly appreciated!
Thanks, Robert