Is the mailbox created on Exchange servers?
If so, you can use the command New-MailboxExportRequest provided by DSPatrick to export Outlook items to .pst file.
Additionally, you need the Mailbox Import Export role to get the permission to use this cmdlet. You can add the Mailbox Import Export role to a role group, or grant Mailbox Import Export role to administrator or other users who perform this procedure:
New-ManagementRoleAssignment -Role "Mailbox Import Export" -User username
Here is a blog for your reference: How to Export Exchange Mailbox to PST using PowerShell Commands.
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