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As my research, the cmdlet New-MailboxExportRequest seem doesn’t exist in Exchange Online. That cmdlet is only for on‑premises Exchange Server. That’s why PowerShell says it can’t find it even after Connect-ExchangeOnline. Microsoft’s docs explicitly state: “This cmdlet is available only in on‑premises Exchange.”
You can refer via: New-MailboxExportRequest (ExchangePowerShell) | Microsoft Learn
For exporting Exchange Online mailboxes to .PST files, I have not found any directly supported method for exporting mailbox content to PST yet. The mailbox export functionality in the Exchange Admin Center (EAC) is primarily intended for managing mailboxes, rather than exporting their contents.
To export emails from mailboxes, you may need to use the Microsoft Purview eDiscovery tool. This method allows you to export mailbox content efficiently by following the steps provided in the eDiscovery workflow.
Reference: How to Export an Office 365 Mailbox to PST - [Step-by-Step].
Note: Microsoft is providing this information as a convenience to you. These sites are not controlled by Microsoft, and Microsoft cannot make any representations regarding the quality, safety, or suitability of any software or information found there. Please ensure that you fully understand the risks before using any suggestions from the above link.
Additionally, if you do not need to export the contents of multiple mailboxes simultaneously, you can also perform the export directly in the Outlook client. Using the steps provided in Export emails, contacts, and calendar items to Outlook using a .pst file - Microsoft Support, you can complete the export quickly and efficiently, which could save you a significant amount of time.
I hope this helps.
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