The standard Moodle message "boxes" are per user. Therefore not associated to courses. The additional plug-in Mail https://moodle.org/plugins/local_mail claims to do that. Never tested myself.
In reply to Visvanath Ratnaweera
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In reply to Deleted user
Re: Ang: Re: Message from student - which course?
by Visvanath Ratnaweera -
Test, What? Who? If you think this plug-in has functions you are looking for, you have to test it. Then don't forget to come back and report your findings.
And just to add to what Visvanath said, look at the number of downloads and how up to date the plugin is (for which versions) That might also give you an idea of how good it probably is.