What firewall is being used on his computer? He needs to make sure that the minecraft port is open on his computer. That may be difficult in that I'm not sure if the firewall would be able to tell that a program running under Java should have open access and the port assigned by "Open to LAN" is randomly different each time that is done.
If you have a spare computer, or one with more than 4 GB RAM and 64-bit OS that could run client and server, you might consider learning to run a separate minecraft server. The server should be in its own folder and once it runs to set up its files (and create a default world), you can add an existing single player world to it and change to that world by making sure that world folder name is something other than "world", copy that folder to the folder with the server, then change level-name=world to the other world folder name in server.properites file.