Light isn't a constant rigid line, it's made of photons, which are particles that share some characteristics with waves, but they have no m and travel at a constant speed. When the spaceship moves it isn't moving any of the photons, it is emitting new photons, starting from a slightly different point in space. Which gives the effect of beam moving, but it is made of entirely different photons, hope that helped, I'm a bit to tired to be discussing physics though...
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