github fork a repo branch

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I don’t know a native way yet, but you can do it following this recipe:

  • Fork the repository in question (called ‘upstream’) on the GitHub website to your workspace there.
  • Run the GitHub desktop application and clone the repository onto your PC.
  • Use the GitHub desktop application to open a shell in the repository. (The git commands are not available from the default PowerShell unless you configure that manually.)
  • Set the source repository as upstream:

    git remote add upstream https://github.com/{user}/{source-repo}.git
    
  • Fetch the full upstream repository. (Right now, you only have a copy of its master branch.)

    git fetch upstream
    
  • Make your file system copy the branch you want and give it any name:

    git checkout upstream/{branch-in-question}
    git checkout -b temporary
    
  • Publish your repo using the GitHub desktop application.

  • On the GitHub website, open your repository and click ‘settings’.

  • Change the “Default branch” to ‘temporary’. (Just change the drop-down menu, you don’t need to click the “Rename” button.)
  • Go back to your repository, go to the ‘branches’ tab, now you can delete the “master” branch.
  • Delete the master branch on your shell and make a new master branch:

    git branch -d master
    git branch master
    git checkout master
    git -d temporary
    
  • Once more, publish your repo using the GitHub desktop application.

  • On the GitHub website, open your repository and click ‘settings’.

  • Change the “Default branch” back to the (new) ‘master’ branch.
  • Go back to your repository, go to the ‘branches’ tab, now you can delete the “temporary” branch.

This should be what you were looking for. Perhaps GitHub will provide a more convenient way to do this in future (e.g., clicking “Fork” from a project’s branch results in exactly this behaviour).