You need a rewrite rule. They and their placement in different ruleset numbers vary by sendmail version. Each rewrite rule runs until it does nothing, recursively, so be careful. They are a bit like sed s, but I forget already, and have to google. SMTP sendmail.cf
Addresses are already reformatted by the time most rewrite rules see them, adding to the fun. "echo 'some_addr'|sendmail -bt" returns some indication of what rules are up to. (mnemonic - Become Tester -bt)

So, find out which sendmail version you have, and google around for sendmail rewrite rule ruleset.

Not linked to the web, but I stole this a few decades back, for an old sendmail version: http://davidgpickett.home.comcast.ne...l_tutorial.txt

This looks just right for you: http://www.sendmail.org/~ca/email/en...#SM-MASQUERADE