The student when sends the private message to the instructor then the instructor gets the notification from the site that the following student has send you this message and the instructor receives the email notification because instructor has enabled the settings.
Therefore the email is triggered by the site and therefore by site email address not by student email address. Now when the instructor clicks reply in the email, the reply goes to site email address and not student email address.
Conclusion: Can you send private message to instructor through emails in wplms or at least reply by email?
Come on! Nobody wants this? Or have people figured a way :)