Delete Assigned E-mail, Keep Relationship

When an e-mail record is imported, it is assigned to a user, and related to an account. At this point, the e-mail appears in the assigned user’s inbox as unread, and in the history of the related record. If the assigned user deletes the e-mail, it is removed from both locations. What is the best way for the user to get the e-mail out of their inbox, but maintain the relationship between the message and the record under history?

(Also, why can’t a message be dragged-dropped into a user’s inbox subfolder?)