Hi Stitch-in-Time,
I understand you have tried updating the browser, but the same issue persists. Since the user can reply, forward emails well on an IE browser, this indicates that Office 365 service has been working well, and this is probably a browser issue, such as some limitations on Safari.
I've searched a lot, and noticed some users who have similar issue post their problem on Apple forum, and they resolved the issue by changing some settings on the browsers, such as add-ins. Therefore, I recommend you try involving apple support to see if they will offer further help, then the issue can be resolved more quickly.
Meanwhile, if you need further assistance, please feel free to post back, and I'll try my best to help you.
Thanks,
Vivian Wang