How are you adding the shared mailbox in Outlook? I would recommend you do so via the File > Add account functionality, which will add the shared mailbox as a fully fledged account and will in turn support all the features. I just tested and I cannot reproduce the behavior you are describing above with this method.
You will need Full access permissions on the shared mailbox for this method. Also, the "new" Outlook client does not yet support it (feature should be coming in March).