Short answer: You can't do that.
Back in the old days, mail servers used to be quite relaxed about posting mail whenever anyone asked them to, but then SPAM happened and people realised that it was actually quite important to check that the person sending an email is actually the person whose address appears in the From:
header.
There are now several mechanisms in place that make it very difficult to spoof a sender email address. These include:
Sender Policy Framework (SPF): An email validation system that works by placing restrictions on the IP addresses authorised to send email from a particular email address. If you try sending email from an IP address not associated with the legitimate owner of an email address, your mail will be rejected.
DomainKeys Identified Mail (DKIM): A method for confirming that emails claiming to have originated from a particular mail server really did originate from that server.
Mail transfer agent restrictions: These days, most MTAs are configured to only accept emails from people who it already knows. (This is why you're seeing a Sender address rejected: not owned by user
error message).
Instead, your best option — essentially your only option — is to put your own email address in the From:
header, and send the email from your own mail server. If you want the reply to go to someone else, add a Reply-To:
header containing their email address.