HI @3627583175
Unfortunately, I don't believe this is possible. The Inbox tool in Canvas isn't an email system, it's a messaging system. So, it doesn't have the robust features you would expect from a full email client.
You mentioned you can filter by student, did you know you can also filter by course?
https://community.canvaslms.com/t5/Instructor-Guide/How-do-I-filter-conversations-as-an-instructor/t...
Also, it is my understanding that messages are never removed from Canvas unless purposefully deleted. So, having them in Canvas is in essence an archive. This is why I personally require students to use the Inbox messaging tool for all course communications as it's archived in Canvas and linked to the course instead of mixed up in my school email account.
You may want to submit your support for this feature request. Export Canvas Messages
https://community.canvaslms.com/t5/Idea-Conversations/Export-Canvas-Messages/idi-p/363571
This discussion post is outdated and has been archived. Please use the Community question forums and official documentation for the most current and accurate information.