by Hartmut Scherer.
Hello Sebastian,
Sorry for my delayed answer. I overlooked your reply in the daily Moodle digest. I am using Moodle 2.9.1. This may differ from your Moodle version.
In a course, I open Assignment > Edit settings and scroll down to Notifications and select "Yes" in Default setting for "Notify students" and save it.
As a student I submit my assignment. Now when I log in as a teacher and grade the assignment, the student will be notified. This is the message that the student received.
With kind regards,
Hartmut