We have the impression that something has changed on Exchange back-end.
All of a sudden outgoing mails from our Shared Mailbox have strange behaviours. Mails keep being stuck in outbox but are also delivered.
Several of our users have reposrted this issue for various mailboxes. They all use Outlook 2016 MSI.
Are you experiencing the same issue on OWA? Is this Exchange Online or on premise?
You can try with a new Outlook profile to see if the issue is within the current client profile.
is the account in outlook as an account while is it shared with another account in the profile and would sync on its own via automapping? If so, remove the share or remove the account.
It appeared to be caused by the change in the behaviour of sent items of shared mailboxes (which can be controlled server side now) and by the fact that caching was enabled for shared folders.
Most issues have been resolved.