[Exim] Web based Email and Normal email using same mailboxes…

We have a desire to allow people to access their mailboxes remotely
using a Web based Interface, but to also allow them when they are in
the office to access their mailboxes using the normal interface
(Mutt in this case).

I'm looking for something that would permit either. We are using
Exim on all of the machines in question.

I've seen a bunch of web mail packages, but all of them are based upon
IMAP/POP type mailboxes.