Well, actually, simplest would be your projectile not moving at all, being local, and you moving the system itself.
As for the beam:
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Add a user variable vector on the left
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Emitter update group / Beam emitter setup / set the end point to your variable
Now you can just tell your Niagara particle system component through set vector parameter where you want the beam to end. You can even set it to Absolute so you only need to add the position once or when it changes for some reason.