How to combine imap.work.edu with smtp.gmail.com?

[macbook123]

I can't send emails through my IMAP account because it's VPN restricted and the built-in VPN client is not accepted. So I'm trying to use smtp.gmail.com:587 as outgoing mail server, while ingoing is my work's IMAP server (I'd like to keep it this way because it means emails erased on my Iphone will also be erased on the Mac and vice versa). When trying to send this way the "Sending" bar on the iPhone says "sending message..." and it's growing very slowly. After about 10 minutes (!) the bar is full, and eventually vanishes, but there is no "Sent Mail" sound and the mail has indeed not been send out.

Any idea what's wrong?

 

[upaymeifixit]

I thought it has to authenticate with the gmail smtp servers as well as your imap server. I don't know how you would do this on the iPhone though.