It looks like that diagram doesn't provide enough information.
He would need two separate relay circuits: one for the low beams and another for the high beams. The high beam and low beam voltages from the headlight switch would have to be substituted for the "ANY switched +12v lead" connections in the drawing. Also, the "FAN +12V wire..." connections would have to be connected to the low beam power on the first circuit and the high beam power on the second circuit. The "FAN +12V wire..." connection would have to go to either both low beam filaments or both high beam filaments. That's why each pair of filaments would require their own relay setup.
The fact that he already bought a new alternator and regulator suggests to me that he doesn't yet have the experience to be able to convert your schematic to something he can use for his headlights.
BTW...I have used this relay setup on my two old cars and the really brighten the headlights. You don't need be fixing a headlight problem to see a big improvement!