github
schacon created a project on GitHub called "showoff". Later, puppetlabs created a fork. Eventually, schacon made puppetlabs the official maintainers.
If you look at the repos now, they show that schacon's repo is a fork of puppetlabs' repo. In other words, the fork is shown as the original and vice versa.
How is this done?
You can try and reverse how pull requests happen.
Issue a Pull Request
By default this will be your fork on the right (head repo) requesting to push its commits and changes to the original repo (base repo) on the left.
Click the drop down for both base repo and head repo and select each other's repos.
You want yours listed on the left (accepting changes) while the original repository is on the right (the one with changes to push). As illustrated in this image:
Send the pull request
If your fork has not had any changes, you should be able to automatically accept the merge.
If your code somehow conflicts or is not quite clean enough, then this will not work to update via the GitHub web interface and you will need grab the code and resolve any conflicts on your machine before pushing back to your fork.
Just write a small script with Github API. That should be fairly easy.
Best Answer
This can only be done by sending a request directly to GitHub Support.
It's not a normal procedure that accounts can do themselves and requires GitHub to change the designation.
It's a different step compared to transferring a repo which you can do yourself if you have the correct permissions.