The reason that the shared mailbox appears in Outlook, but does not appear in the Outlook account settings, is that auto-mapping is enabled by default when a user is granted access to a shared mailbox or to another user’s mailbox. When auto-mapping is enabled, Outlook receives extra information in the Autodiscover response that tells it to open the additional mailbox.
1. Use Get-MailboxPermission to verify the permission level
Get-MailboxPermission -Identity "Mailbox Name" -User username | fl
2. Next, use Remove-MailboxPermission to remove the mailbox permission for the user.
Remove-MailboxPermission -Identity "Mailbox Name" -User username -AccessRights FullAccess
3. Re-add the mailbox permission with the -AutoMapping switch
Add-MailboxPermission -Identity "Mailbox Name" -User username -AccessRights FullAccess -AutoMapping:$false
4. Allow some time for user to pickup that via Outlook Autodicovery
5. To view the list of auto-mapped users for a mailbox run:
Get-ADUser -Filter {Name -eq "Mailbox Name"} -Properties msExchDelegateListLink | Select -ExpandProperty msExchDelegateListLink