Using Outlook for iOS in business environments for email and scheduling
I also have exactly the same issue. Tried everything except reinstalling the app.
You can forward the sent email to yourself and it will show in your imap/inbox as well as the Outlook app inbox.
If you try to move the sent email to your inbox it will show in the Outlook app inbox, but doesnt show in the imap/inbox (via email app, desktop, webmail, etc)
Weird.....