You can’t send email to external address if you don’t add send connector to Exchange Server 2010. I will show you how you can easily add send connector with Powershell:

New-SendConnector –Name ‘External’ –Usage ‘Internet’ –AddressSpaces ‘SMTP:*;1’
–DNSRoutingEnabled $true –UseExternalDNSServersEnabled $false –Fqdn ‘mail.yusufozturk.info’

You can modify name and fqdn. My FQDN is the external domain name of my Exchange Server 2010.

You can add send connector to Exchange Server 2010 with Powershell:

New-SendConnector –Name ‘External’ –Usage ‘Internet’ –AddressSpaces ‘SMTP:*;1’ –DNSRoutingEnabled $true –UseExternalDNSServersEnabled $false –Fqdn ‘mail.yusufozturk.info’

You can change -Usage and -AddressSpaces for your needs.