For the love of sanity why? The moon is 770 times as far away, which means you'd need a laser almost 600,000 times more powerful than one in Low Earth Orbit to deliver the same "punch". (Lasers spread out like any other beam of light, so inverse square law applies). Your aiming mechanism also needs to be magnitudes more accurate. If you're running this off solar power, then the moon based laser is going to be out of commission half the time, and is not going to be at peak energy most of the time. Furthermore, the launch costs are going to be astronomical.
A satellite based system can be in perpetual sunlight, with the solar panels constantly at the optimum angle for energy collection. You're right on top of the target, so aiming is easier and power delivered on target is greater.