[exim] Repost - Help with router condition - Repost

Hello all,

I need a little help.

My setup:

Linux Debian Sid box behind a firewall at work. The firewall prevents me
from doing dns lookups, giving me troubles to make exim work as I need
it to. I implemented a smtp auth via login for my box via pam modules,
for learning purpose here and to install at home for preventing open
relay, as I'm not firewalled there (ppp connection, no dsl at the time).

My problem:

For dns lookup reasons, I ought to use a smarthost. So far so good,
I managed that without much pain. But, when I use my email client
(Mozilla Thunderbird) to send via exim here, I can do auth via login as
asked, but it doesn't use my remote smtp router, using dnslookup
instead, which doesn't work as explained.
This problem doesn't appear via mutt which doesn't do auth.

My question:

Is there a way to make a condition in the router to test for
authenticated smtp submission, to route mail from authenticated
mechanism to route to smarthost?

I hope my question is clear.

Many thanks for reading.