The easiest would be to just have them change the remote associated with their local copy of the repository and then push into the new repository. That way they'll keep all their history. They can then just delete the old repository on GitHub.
So instead of
git checkout email@example.com:organization/new_repo.git
they would run
git remote set-url origin firstname.lastname@example.org:organization/new_repo.git
Then the next
git push will go to the new repository and the old one can be deleted.