No Address Rewriting for internal mail howto?

In my office I have an adsl line with one address email
(pippo@public.address) provide by
my ISP.
I installed an internal mail server with linux:
1) smtp server --> postfix
2) pop3 server --> qpopper

I have an internal domain (@studio.local) with 5 internal email (user1,
user2....), my problem is the follow: when send an email outside no problem
the sender_canonical
settings work fine. But if an internal user (user1) sends an email to
another internal user, this one receive the email from pubblic email
address. How can fix this disadvantage.
Best Regards

this my file setting:

sender_canonical:
user1@studio.local pippo@public.address
user2@studio.local pippo@public.address
user3@studio.local pippo@public.address
.....

virtual:
pippo@public.address user1@studio.local, user2@studio.local,
user3@tudio.local