Let's roll back, why do you want to update your drive in the first place? Is there anything wrong with it?
Your drive is an OEM considering the firmware 8.B8. Current retail firmware for GBW-H20L is YG01. Even if you find an official firmware for GBW-H20L, flashing might not work (not 100% sure). If you want to update the firmware I would suggest calling HP. Otherwise if you want to crossflash to GGW-H20L do it with your own risk. I have to say that the crossflash procedure is safe but you will void the warranty.
By the way, GBW-H20L and GGW-H20L use the same hardware, same pickup, same chipset and PCB.