Hi raminsr,
Receiving:
The error "550 5.7.54" indicates that the receive connector does not allow an anonymous or unauthenticated sender to relay to external address.
Are you using the Edge server to receive inbound messages? You should verify which receive connector reject the inbound message and run the following command for it to assign the permission:
Get-ReceiveConnector name1 | Add-ADPermission -User "NT Authority\ANONYMOUS LOGON" -ExtendedRights "Ms-Exch-SMTP-Accept-Any-Recipient"
Sending:
When the subscription is done, it creates a Send connector named EdgeSync - <Site Name> to Internet that's configured to relay messages from the Exchange organization to the Internet.
Did you get any NDR when sending fails? Or was the message stuck in Outbox?
Please search the message traching log for more information:
Get-MessageTrackingLog -ResultSize Unlimited -Start "3/28/2015 8:00AM" -End "3/28/2015 5:00PM" -Sender "pat@contoso.com"|fl
Regards,
Eric Yin
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