Mircosoft remote desktop v.10 app for mac. You can send files and folders by attaching them to an email message. When you attach a folder, Outlook 2016 for Mac compresses the contents of the folder into a single.zip file. In your message, on the Message tab, click Attach File. Outlook 2016 for Mac gets Modern Attachments New to the Insider Fast channel, Outlook 2016 for Mac now supports Modern Attachments with OneDrive, OneDrive for Business and SharePoint integration. It should make it's way into the current channel in due course.
I would verify that their Exchange account is the only account within outlook. From a few different places it looks like it could be something stuck in Drafts too (although you said you checked there). Possibly removing the account and re-adding it in Outlook could be the quick fix to it (although they would lose their saved autocompletion which a lot of people complain when they lose it).
Im running 2016 on probably 25 Mac's and haven't seen this issue yet, but I have had weird issues with Outlook in general that aren't worth the time messing with and just adding the account back again will fix saving all of our times.