Thank you for your kind help but i'm a system administrator, so yes, i already tried a lot of things before posting.
I also tried to identify every root id device in the system and none of them correspond to a bluetooth device. I have to suppose that there are some models of HP 650 notebook that doesn't have bluetooth built-in. That's all we know
Or maybe there's a hidden setting somewhere (very essential bios and no reference to bluetooth at all) that enables the bluetooth radio device. Anyway, a 5$ usb adapter will solve the problem. Thank you anyway