Exchange 2010 Setup

We have installed a new SBS2011 Standard server for a customer.  Software installation completed without any known issues.  User accounts and mailboxes have been added.  When their old server crashed, they used the AppRiver Exchange 2010 service to keep e-mail access while the new server was setup and installed.  When the Exchange setup was completed, the AppRiver support team used telnet commands to test sending messages to the new server.  Telnet, “ehlo”, and "mail from:"  commands work OK.  When the telnet "rcpt to:" command is entered, the reply is "550 5.7.1 Unable to relay."  This command has been tried with more than one e-mail address.  We did get the command to work one time when we entered a range of 0.0.0.0-255.255.255.255 in the receive connector.  Is this acceptable or are we opening the door for more problems?

Receive and send connectors have been created.  The receive connector uses I.P. addresses supplied by AppRiver.  We have checked the receive connectors and they appear to be correct.  The permission groups checked are Anonymous and Exchange users.  We are wondering if some question or configuration was missed or entered wrong during the server or Exchange setup.  

What do we need to check to resolve the “Unable to Relay” issue?  Is there a checklist or reference document we can use to verify the Exchange server configuration?  Is there a “tool” that can check Exchange and identify problems?

I would also appreciate any suggestions on testing both receiving and sending messages before the AppRiver service is stopped.  We would like to know everything is working before redirecting the mail to the new server.

Any suggestions will be appreciated.