The administration and maintenance of Microsoft Exchange Server to ensure secure, reliable, and efficient email and collaboration services across an organization.
Based on my research, exporting the Auth certificate together with its private key by using the Export-ExchangeCertificate cmdlet is no longer supported.
As an alternative, you may export the certificate by using the Export-PfxCertificate cmdlet, which is the supported approach. You can find more information about this cmdlet in the following reference: https://learn.microsoft.com/en-us/powershell/module/pki/export-pfxcertificate?view=windowsserver202…
Another option is to use the MonitorExchangeAuthCertificate.ps1 script, which can help you review and manage the Auth certificate status.
For additional context and official guidance, you may also refer to Auth Certificate export through Exchange cmdlet is no longer supported - Microsoft Support
I hope this information helps you move forward.
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