As others have said unscrew the back, place the joystick back on. I'd recommend getting a new one sent out but given the slight break on it you might be able to get away with using the same one. I'm guessing he is either chucked it at a wall or is a dog and it's his favourite chew toy. If you use the old joystick be warned that the internals will be more exposed and dirt more likely to collect inside.

With it not being an official nintendo Pro controller you probably won't need to get a tri screwdriver that you need for most Nintendo products. So won't be too hard to fix. You may need to talk with your brother though about not abusing his tech.