email realy to external address

our mail server is running exchange 2010 and our backup  server application wan to send the backup status details to internal and external users for above purpose  . all the internal email address getting the  status . but all the external email getting really issue  . how can I our backup server to relay email though exchange server . what is the best way to go with the solution

I have tried creating contact as external email and result was the same .
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This link shows it step by step how to allow ONLY ONE IP number to have full relay access:
curAuthor Commented:
do we need to restart the IS service to work the connector ?

permission  group  section  , I have selected anonymous users only . do I have to select the exchange users and servers as well

my sending server is sql based  .net application pushing the email to exchange server

still not working . I didn't restart the server
curAuthor Commented:
we have spam filter as well  ?? do we need to add any thing over there  .
email that I have created to send the email from the application working fine email level
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Restart the server if possible yes. Or if the server needs to be up 24/7, individual Exchange/SMTP services restart should suffice.
curAuthor Commented:
most of the time our exchange server information store restart will not work while server is up . service level service restart will hung . as a result we restart the server and then working

is that the normal

coming back to the rely issue. still my server rely not working . I have select the basic authentication  and anonymous   , still I will end up with the same error

System.Net.Mail.SmtpFailedRecipientException: Mailbox unavailable. The server response was: 5.7.1 Unable to relay

we have multiple network card in the exchange server  due to the ISP hosted server  setup
Assuming this error "5.7.1 Unable to relay" is a response from your server, when you use your application on another PC or server in the same network, that PC/Server's IP was still not added properly to the allowed IP's in the relay section.
Also, I tested it again myself. It works if you follow the steps correctly. But please note, SBS by default has TOO many receive connectors setup and they will overlap, and hence, the new receive connector will do nothing. Remove or disable unnecessary ones.

Make sure you only have one connector to receive email (from all internet IP's) for local delivery (test it from remote, that it WILL deliver local emails, but reject relay emails).
If this is the only rule, then add one more connector according to the page I posted earlier. Now there probably won't be any conflict, and ONLY the IP's you mentioned will be able to send to any email address.

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curAuthor Commented:
I have manage to find the issue . we need to run the shell script to work the connector
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