Messaging FAQ
From MoodleDocs
How can admins view student messages?
See the Using Moodle discussion How can I see student messages?.
How can messaging be restricted to teachers only?
To limit messaging to specific users, you can change the site:sendmessage capability for the authenticated user role from allow to not set, then create a new role with site:sendmessage allowed and assign this to selected users in the system context. See the Blogger role for a similar case, where blogging is limited to specific users.
See also
- Using Moodle Messaging forum