Hi @Evert van Hoften ,
Recently I've been running into the issue that a few users can't view the private items in a shared mailbox calendar.
Does this affect all delegates of this shared mailbox or only some particular users have this issue?
How about Outlook on the web, can the users see the private items there?
From what I am aware of, using the SharingPermissionFlags "Delegate,CanViewPrivateItems" should be enough for it to work, so it doesn't look like an issue with the permission. Given this, if the problematic users are currently running Outlook in Exchange cached mode, it's recommended to test on one machine by switching to Exchange Online mode when the issue occurs and see if it can help.
Besides, another workaround worth trying is to add the shared mailbox as an additional account in Outlook by using the email address and password of the user who has permission for that mailbox. For detailed steps, you can refer to: How to add a shared mailbox as additional account in Outlook(Please Note: Since the web site is not hosted by Microsoft, the link may change without notice. Microsoft does not guarantee the accuracy of this information.)
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