When you’re on H1-B you’re applying for the green card through your employer, which is a multi-year process. So even if you find an employer who will sponsor it, you’ll be going back to the end of the line.
Or are you talking about green cards, which is a completely different thing?
I thought you were talking about transferring the green card process, because I was talking about the green card process. Transfer is possible, but you have to be past a certain point that takes probably a couple of years, which is pretty good compared to how long I had to wait way back when.