The Hubble telescope's sensors are much too sensitive to survive the damage they'd suffer if pointed at the moon.
Many hundreds of pounds of lunar soil and rock, portions even today being subjected tovery critical laboratory analysis world-wide, are ample evidence that this conpiracy theory is just that.
The procedures of their analysis are not unlike those which might have to be used to prove that your parents are really the very same people in whose house you grew up.
Prove to everyone's satisfaction that you were not left on your "parent's" doorstep by some roving band of alien gypsies.