I have used Thunderbird till recently. And the mail rules within thunderbird did not apply to / did not work on 'sent' messages. Such messages had to be moved manually to the relevant folder.
It appears it is the same for Outlook. Although the detailed settings possible in Outlook does allow for setting up of 'sent' mail to be automatically moved to a specific folder.
Can anyone confirm that Rules work/don't work on 'sent' messages.