Sync Repositories Gitlab <--> github

Hi, I can create a new repository in gitlab or I can import any repository from github, google code and so on. When I have finished this steps the repos are cloned to my own gitlab. Now I working on my gitlab instance and make a lot of commits. Now I want that my commits from gitlab are applied to the original repos from github. Other github member see my changes. How should I configure my gitlab instance that it trigger pushes and pulls regular?

Important: I does not mean to migrate my github repos. I want to use my own gitlab instance as my single-point application for both services (my own gitlab and old github repos that are not closed atm)

You need to make a GitHub hook. Read