How to setup remote desktop connection permission for systems outside my local network?

"As the remote desktop is working internally, the problem must be between the computer and router.

First I would test the port is open using Can You See Me or telnet. If you receive no response, then have a look at the routers firewall settings, it maybe blocking the incoming connection.

One other possibility is your ISP maybe blocking port 3389."

Have you checked the firewall on the Windows 7 computer to make sure it allows remote connections from the internet. On my computer I have three profiles for connections when setting up the firewall: Domain, Private and Public. If the port is not open for the Public profile, that may explain the issue.