it will not work
it does not matter how big the laser is because as the earth turns, being able to even find the thing much less stay on it, is going to be impossible. THERE ARE TOO MANY VARIABLES FOR MOVEMENT.
The equator rotates at 1000 miles per hour, less going north south, near zero at the poles. So an astro from the space station is going to put the stampship say out on a stick and down on earth they are going to spot it and zap it from time to time, right? WRONG.
funny thing is this - they will get the money for the project and do some periodic zapping and tell the world that everything is going according to plans and calcs and they themselves will really never know if that is correct. Yeah, after earth changes orbit, season, revolution etc they are going to home in on a button light years away no problem. CAN I GET A REFUND?