Hi, since this is a bit time-consuming to always check mailbox for possible WZS-internal mail, the user should get an alert like "1 new message" if there is a new message incoming.
I've had it many times that I wrote to users and they apologized after 4 weeks that they never looked in their mailbox before.

How could they, anyway, if they did not know they got a new message?
As I wrote above, users will only very rarely check haphazardly whether they got new mail.

And no, the e-mail notification that there is a new message in the mailbox won't be sufficient.
Please think about users on mobile devices who can only see WZS but can't have their mailer open the very same time - so they will never see it.