There should be an optional text box in the mail header somewhere next to Subject field. Mail sender can enter a folder name in that before sending mail. For e.g. HR\DressCode, Finance\Policy, ProjectName\releaseName etc.
When he hits the send button, the sent mail is parked automatically in the folder.
When recepient receives the mail, he/she also sees the suggested folder in the mail header and there should be a button/link next to it, onclicking which the mail will also moved to same folder in his mail box. Folder hierarcy will be created if needed.
This would save lot of time tidying up inbox, especially when mid sized teams exchange lots of mails among team members.