You may want to create an open mail relay in Exchange to allow other servers to relay mail through your exchange server.
There are 2 steps:-
1. Create a new receive connector in the management console. In the “permission groups” tab, check anonymous permission and put the IP address of the server that you want to permit relay from. In the example below I have called the receive connector “Allowed Relays”
2. Open the exchange management shell and enter the command: Get-ReceiveConnector “Allowed Relays” | Add-ADPermission -User “NT AUTHORITY\ANONYMOUS LOGON” -ExtendedRights “Ms-Exch-SMTP-Accept-Any-Recipient”