This quick TIP will guide us to move a repository to the new one.
1/ Checkout everything from the old repository
git clone --mirror <url to OLD repo>
2/ Push everything to the new repository
git push --mirror <url to NEW repo>
3/ Update remote origin
Remove old remote origin
git remote rm origin
Replace remote origin by new repository
git remote add origin <url to NEW repo>
Done, enjoy your new repository.