Make sure you have this git alias
git config --global alias.clone-branches '! git branch -a | sed -n "/\/HEAD /d; /\/master$/d; /remotes/p;" | xargs -L1 git checkout -t'
Clone the remote, pull all branches, change the remote, filter your directory, push
git clone git@github.com:user/existing-repo.git new-repo
cd new-repo
git clone-branches
git remote rm origin