Emails marked by a sender as Private and sent to Office 365 Shared Mailbox are not visible in Outlook for users with Full Access permissions. The only indication about these emails is increasing unread item count in the shared mailbox Inbox folder.
There doesn't appear to be a proper resolution for this as of now. When sharing a normal user's mailbox you can select option Delegate can see my private emails (Outlook > File > Accounts Settings > Delegate Access). This, unfortunately, doesn't work for Office 365 shared mailbox.
One workaround is to convert the shared mailbox in question to a user mailbox, add it to Outlook and enable above delegate access option, then convert it back to a shared mailbox.
Another workaround is to simply to access the shared mailbox in Outlook Web Access (webmail) where private emails are displayed normally.
Microsoft Office 365