The tiny screw method works. We dipped it in dish soap, made a tiny groove with a thumb tack and then threaded a very small screw. Used two pairs of plyers, one on the arm and one on the screw, and pulled the broken hand out with no issue.
I extracted two broken hand stumps with a hot needle and replaced them with unbroken hands from less important or otherwise broken figures.
Position the figure's arm pointing straight out and remove accessories that might fall off.
Hold sewing needle with pliers over stove until glowing hot.
Plunge hot needle into hand stump at an angle.
The Lego Company is usually very good about replacing broken and defective parts for free. In the case of expensive electronic parts such as this, in my experience, they will sometimes request you send them the broken/defective one. If this is the case, they will make it easy for you and send everything you need to do so with your replacement. Because ...
The best and most effective technique I've come across is to use a bit of nail varnish on the inner anti-stud of the helmet piece, as Tonk explained on his blog TonksToysBlog. Just be sure to apply a very tiny amount and give it plenty of time to dry.
Also, if it matters to you, the helmet you have pictured does not go to the figure pictured. The figure is ...