If you want to use authentication relay, you need to bind certificate to Client Frontend Connector first, you could have a look about this article.
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Then you need to create an Exchange on-premises mailbox rather than remote mailbox to relay email.
After that, use "Send-MailMessage" command to check whether all configurations are correct. If there exist issue with it, you could check the receiver connector log (%ExchangeInstallPath%TransportRoles\Logs\FrontEnd\ProtocolLog\SmtpReceive) to find why you cannot relay email.
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