After searching a bit for this, I thought I’d share the solution.

I have mail automatically forwarded from other email addresses (at other domains) to a Google Apps email address. The problem is, even though I set my IMAP client (Thunderbird) to say “From: otheraddress@otherdomain.com”, Google automatically rewrites that to my Google Apps address when I use their SMTP server.

This is actually a good feature, it prevents spam by making it impossible to send an email *from* google’s servers while pretending you’re joe@fbi.gov.

Google have worked an elegant solution to this. In the user’s gmail/google apps account settings, under “Accounts”, you can add addresses for “Send Mail As:”. Google will send an email with a code to any address you with to impersonate, and clicking the link or typing back the code will activate that address. You can then make one of them the default one, which will be used for emails sent via SMTP from your regular email clients.