Give users full mailbox access to the shared mailbox and ensure the shared mailbox is not cached
It will show up automatically in the folder view. Do not add as an additional profile in Outlook.
Uncheck "Download Shared Folders" should be unchecked. If its checked, uncheck and restart outlook
https://support.microsoft.com/en-us/help/3115602/performance-and-synchronization-problems-when-you-work-with-folders-in
Other things of note, you can enable it so that sent items always go to the sent items of the shared mailbox if you want:
https://learn.microsoft.com/en-us/exchange/troubleshoot/shared-mailboxes/sent-mail-is-not-saved
I would also consider recreating the Outlook profile if it continues. Items that appear to be stuck in Outbox are a symptom.