I had the opposite problem and finally had to create my own bash shell script for the company to migrate the hundred of repos from Github to Gitlab due to a change in the company policy.
The script use the Gitlab API to remotely create a repo, and push the Github repo into it.
There is no README.md file yet, but the sh is well documented.
The same thing can be done opposite way I imagine. Hope this could help.
https://github.com/mahmalsami/migrate-github-gitlab/blob/master/migrate.sh