SMTP Forwarding rules

We have a requirement to forward physician emails to their private email accounts and utilize SMTP forwarding, which works fine. Now we need to modify the forwarding to only allow internal originating emails to be forwarded to their private accounts and none of the ones received from an external source. Example would be nofoo.com is our domain if the email is from xyz@nofoo.com then it is allowed to be forwarded, via SMTP forwarding to the private account.  If the email is from hello@gmail.com then is is NOT allowed to be forwarded.  We have tried several things