Q:

github push code from one repo to another

Create a new repo at github.
Clone the repo from fedorahosted to your local machine.
git remote rename origin upstream
git remote add origin URL_TO_GITHUB_REPO
git push origin master
Now you can work with it just like any other github repo. 
To pull in patches from upstream, 
simply run git pull upstream master && git push origin master.
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cd rhq
git push https://github.com/user/example master:master
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