After reading everything and be being very, very careful with the instructions listed here
https://vkbcontrollers.com/?p=4366
I took extra care when doing the reassembling of the grip (took note of the warning about wires)

I have correctly plugged the USB, loaded the profile " BB_GF-TM(1_85_2)0_79_99 " found here http://ftp.vkb-sim.pro/Profiles/BlackBox/
I have calibrated the axis and saved but the buttons doesn't work

The only different I have from you guide are this round connector that was connected to the screw that secure the connector for the base. (In your picture it seems to be still connected to circuit from Warthog, and in mine it is connected only to the original base connector from the Warthog .

For the LED on the blackbox, I have the top left in blue and the middle right one blinking in red.
If you could tell me what I have done wrong, any help would be appreciated.
Have a nice day.