@username619 - always remember this - GC through employment is based on future employment. It is NOT what you did in the past or currently doing but what you will be doing when you have your GC.
H1B is just a temporary immigration status that lets you work and maintain your immigration status in USA.
You can file GC even if you are in F1 status. I hope we are still talking about GC through employment.
How many company do you really find that is willing to do it?...The burden lies to you and company to prove your process.