Hi @Torza, Michael,
I would suggest creating an Exchange Online retention policy to automatically archive old emails.
Overview of Exchange retention policy: Retention tags and retention policies in Exchange Online
You can add custom retention tags (which decides either to delete or archive emails which reach a certain age) to a retention policy and assign this policy to the user mailbox.
However the in-place archive is empty as the user does not have access to all subfolders because it is giving them an error that "some items are private and cannot be moved"
Is the detailed error message like "Cannot copy this folder because it may contain private items"?
This may be related to shared mailbox, while it does not occupy primary mailbox storage quota.
For more information please refer to this link: "Cannot copy this folder because it may contain private items" error in Outlook
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