Hi @katrien_delangh,

One of your school/institution Canvas administrators can adjust some of the permissions around the inbox.  Specifically, this would be related to the "Conversations - send messages to individual course members" and "Conversations - send messages to entire class" permissions.  There is a caveat listed though, "When disabled, students can still send individual messages to course teachers, course TAs, and students that belong to the same account-level groups."  So, if you have an account level group, perhaps including all of your students, then it sems they would always have access to message each other.

Hope this helps a bit!

-Chris