Github for Windows does mention in the help page that:
GitHub for Windows is optimized to work with GitHub remotes — but if you wish to use a non-GitHub remote, it will work just fine. Set the remote manually in the settings tab and everything else should work as expected. You can also drag in repositories from the file system and GitHub for Windows will respect the configuration of the origin remote.
So you can pull from a non-GitHub repo, like I did in this answer or as illustrated in this blog post.
But from your local clone, you cannot easily push to another repo (like one in your wamp
folder for instance)
it does not support multiple Git remotes and it will only work with the origin remote.
If you wish to push & pull to other remotes, we suggest you use the command line client that is included with the application.
An alternative to command-line would be to use a GUI which does support multiple remote, like SourceTree.
Or you can clone the GitHub repo from the command-line directly in the right folder, and then declare that local repo in your GitHub for Windows
app.
Or you could create a virtual host that has a DocumentRoot
of the Github folder of My Documents
(meaning you don't have to move anything, and can keep using GitHub for Windows as you were).