Will H1 simultaneously be no good after receive GC and do I need

My hu*****and just received his GC last week. He is still using his H1 visa to work with his current employer. I am wondering whether his H1 visa is no good after get his GC and should inform his employer about his new status.

I am holding H4 with an EAU. What status do I hold now, still H4 or what? Do I need to do anything?

Thanks in advance for your information