anonymous user
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What's the detailed version of your Exchange 2016, please check with the following command:
Get-ExchangeServer | Format-List Name,Edition,AdminDisplayVersion
Did you try to relay messages to external users from your application or services?
If so, as AshokM-8240 mentioned, please created a dedicated Receive connector for anonymous relay.
If you just try to send from the user mailbox in your organization, please check if other user mailboxes can send messages to external recipients.
You can use this command to check send connector settings. You can post the screenshot here and don't forget to cover your personal information:
Get-SendConnector|fl
Additionally, I make some modification on the command provided by AshokM-8240. You can use it to list some important information for message tracking:
Get-TransportService|Get-MessageTrackingLog -MessageSubject <subject> -Sender <mailbox address> -Recipients <mailbox address> |select timestamp,EventID,Source,ConnectorID|sort-object Timestamp
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