I want to give an update to this issue.
I am still having multiple users that are not receiving their emails, both Course Invites and Certificate of Completion. I have talked with Instructure's Tech Support multiple times, and they can't see anything wrong with their system.
I have come up with two different solutions to the issue.
For the Course Invites, I am able to go into the course (through Canvas, not Catalog) and view the student. I then reset their password. Then I go to our Catalog URL, sign in as that user, and accept the course invite as if I were the student. Then, I send an email to the student with the new password and step-by-step instructions on how the student can change their password to their own personal password. This has worked so far, however, it is very time consuming.
For the Certificate, I have added step-by-step instructions to the courses that have certificates that walks the students through the process of finding the certificate on their Catalog Dashboards.
I would love to find a solution to this issue, especially from Instructure's side of things. I really like Trina's solution of having the emails come from our institution, or appear that it is coming from our institution, instead of from Instructure Canvas. Most users do not understand what an LMS is, nor do they understand why they are receiving emails from a place called Instructure when they have signed up for a course from our institution.
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