We have a user who is running Outlook for Mac v16.13 (180513). She is an executive assistant to our CEO and has delegate rights to his calendar. He runs Outlook for Windows.
When she creates or modifies a calendar entry on his calendar from Outlook for Mac, it never shows up anywhere but her local copy of Outlook where it was created, UNLESS she modifies an entry that was originally created by our CEO. However, if she logs into OWA she can create/modify any entries and they do show up in her local copy of Outlook for Mac, as well in our CEO's copy of Outlook for Windows.
Essentially, the issue seems to be that Outlook for Mac does not sync entries up to the Office 365 server that she creates on the delegated calendar.
However, if we delete and re-create her Outlook for Mac profile, it will work for a few days, but then suddenly stop working again. This seems to have happened with one of the last few releases of Outlook for Mac, as she's not had this issue in 2.5 years, it's only started happening within the past month or so.