I wonder if it's possible to call our Moodle server from our LAN (192.168.1.201) and from the Internet (22.214.171.124) automatically, e.g., if it's an LAN user it will call 192.168.1.201, or else, 126.96.36.199.
Our Moodle is installed in Windows 2003 Server Enterprise...
In your internal DNS, create a zone with the same name as your public domain; create an A record in this zone with the same FQDN as your moodle will have on the public Internet, but use your internal IP address.
In your external DNS, create an A record with the public IP address you want to use.
On your Internet facing router, perform a NAT or a PAT to your server hosting moodle.
Complex answer on how to do all this on your specific equipment and domain: IMHO should be studied and learned