Outlook rules are only triggered by a select few events. E-mails being read is not one of them.
You could create a VBA script to look for e-mails with the status “read” and then move them to another folder. You’d have to be careful not to move a mail while it was being read, though, as that would cause the window to close or, as the user would report, “my mail disappears when I try to read it!”
I don’t think there’s a good way to accomplish what you want in Outlook. It sounds like the user wants e-mail to behave as something else entirely, like a case in a ticket system or a document in a workflow.