In my experience "on behalf of" is something that email clients show based on difference between From and Sender / Return-Path headers in the email. You can see those headers in Outlook if you right-click on a message in mailbox and select Message Options (in the pop-up dialog look under Internet headers).
The only ways to elimate the difference between those headers is either to send the mail using the other user's account or have your SMTP (outbound email) server modify the headers for you before sending the message outside of your network. Since email headers are not really enforced to be truthful (the reason behind why spamming is so wild and widely spread business), it is technically quite easy to forge those two headers but nevertheless it's likely that no common desktop GUI email application will allow the user to modify them. Pine / Alpine allow doing all that kind of funky stuff, though, so it would be wrong for me to say not any email client would allow that.
Edit: Also, as Ramhound pointed out, the mail server might refuse to send email if the (forged) headers created a conflict between the authenticated user (=you) and the user appearing as the sender (since that could indicate a security breach and/or sending spam and in general would most likely be a violation against the security policy applicable to email users).
