It's not enough to be captured -- the vast majority of launch trajectories that get captured will just go into elliptical orbits. The critical thing is to cancel out the moon's orbital velocity so the projectile escapes the moon with no angular momentum relative to Earth. Your best bet is to launch horizontally at 2.6 km/sec directly backwards from the moon's trajectory around Earth. Assuming a large immovable launcher, you should have a launch window once a month. Slight variations in the speed and the time of launch would allow targeting specific locations.
Actually, there's quite a range of acceptable launch trajectories. -2600m/s is simply the easiest. All you need is to get the periapsis fairly deep in the planet, you don't need to cancel all the orbital velocity.
Note, though, that your launcher can hit at anytime, there is no launch window. It does take a bit of variation to compensate for the moon's wiggles, though.