At the lift-out you should carefully detach the hose from the top of this seacock then remove it from the skin-fitting. Completely dismantle the top by unscrewing, supporting the body in a soft jawed vice and remove the spindle of the handle and the ball-valve. You will undoubtedly find a large amount of calcium salt deposited on the inner surfaces and the spindle surfaces which will need dissolving with de-scaler and polishing with fine emery cloth. This is the probable cause of the handle breaking. These handles are not very robust. This job may take 6 hours to complete so consider a renewal as a near cost effective option. When reassembling add plenty of appropriate grease. As a general maintenance add a few drops of vegetable oil into the head from time to time.