Do admins have the ability to monitor or view some kind of report with all student Canvas communications - especially communications with other students?
As far as I am aware, the only reports regarding communication readily available are those generated via the API, which would be custom made.
If your institution has it enabled, certain users would be able to Masquerade as a user and access their Inbox, but I wouldn't see this as a normal use of the function. Though I have no actual knowledge of the matter with regards to educational certification, I would imagine this could be considered a violation of user confidentiality.
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