Posting using mutt from our primary domain

[ism...@gmail.com]

I have an email account (ism...@gmail.com) with Google mail and just
configured it to forward copies to i...@alaskaclinic.com What I can't
figure out is if I can use the mutt email client and our down SMTP
(postfix running on alaskaclinic.com) to send and receive mail from
hard...@googlegroups.com

Is there a way to merge the mail from a gmail account and googlegroups?

thank you,

Ismet