Unlike so called "DC stators", "AC stators" have one leg of the lighting coil pack connected to ground. So you can't use a bridge rectifier to create full wave rectification here cos the -ve point would share the same connection with the AC lighting coils!
The "AC" regulator, is primitively constructed using only a zener to half wave rectify and clip the peak voltage to around 17v p/p.
Add in an extra diode by cutting the wire in the headset that feeds the dip beam switch (orange on most series 3 and GP) and connect in the diode here. (make sure to get it the right way around) and also solder in the capacitor.
Connect the +ve side of the cap to the -ve side of the diode (cathode) ( Thats the end of the diode with the round band on it if you are using a typical in-line package diode) and also connect this to the dip switch side of the orange wire.).
The -ve side of the cap then needs to connect to chassis.
The loom(supply) side of the cut orange wire now connects to the Anode side of the diode.
This "In series" diode (SR5100 is recommended. Easily avaialable on fleabay) is really only there as a blocker to stop the cap from discharging back into the lighting coils, therefore providing a smoothed DC voltage to the headlamp bulb only.
With an LED bulb, I think 4700uf should be enough but if the lamp still flickers to an unacceptable degree on tickover, then a higher capacitance may be needed.
You'll also need some extra bits of wire for the capacitor connections and some heatshrink tubing to finish the job off properly.
( remember to slide your heatshrink tubing onto the wires first before making your soldered connections. Arrrgh

)
Btw.. Those bulbs that I recommended work from 6v-24vDc.