Should forwarded messages appear in one's sent folder?

Hi all.

I'm running Mail 6.5 under OS X 10.8.4.

I have recently changed my POP mail account to an IMAP one, so this may just possibly be why I'm confused by odd Mail behaviour, but I don't think so.

I just forwarded a message. It was a message that I originally sent to another address, and what I forwarded included the reply I'd received from that first address.

I had expected my forwarded message to automatically appear in my 'Sent' folder, but there is no trace of it there. (Nor anywhere else, it seems.) Messages I actually send -as opposed to forwarding- do appear there though..

Do I need to tweak something in preferences somewhere to get forwarded messages to go into my 'Sent' folder?