This is a very common request. People have internal servers which need to send email.
The MSExchangeTeam blog has a great article about it here:
What I tend to use is the following script:
New-ReceiveConnector -Name ?Internal SMTP Relay? -Usage Custom -Bindings 192.168.200.134:25, 192.168.200.134:587 -Fqdn LDN-ECA-LB.test.com -RemoteIPRanges 192.168.6.25, 172.16.1.12 -Server LDN-ECA-02 ?AuthMechanism TLS, ExternalAuthoritative ?PermissionGroups ExchangeServers ?MaxMessageSize 50MB
This allows the servers at 192.168.6.25 and 172.16.1.12 to relay. The connector will listen on port 25 and 587 at the IP 192.168.200.134.