In my understanding, if you graduated and used TPS mean you are no longer in F1 . Employer can apply for H1b, but your status change will not occur. So, you have to leave the country for H1b status change...happens in H1b visa stamping. GC is possible, I guess, but I am not sure how much legal hassle employer has to take due to TPS, and this could be discouraging factor for them. I have seen Myvisajobs.com listing successful cases from TPS to GC.

Please add what info. you have or will have in the future. Good luck!