The astronaut will have the same mass, but her weight will be less. This is because there is less force from the moon pulling down on her, but she still has the same amount of body parts, blood, etc.
Mass is the amount of matter in any body while weight is the force with which earth attracts everything towards its centre. The quantity of matter inside any object always remains the same that is why it does not change anywhere in the universe but when we move away from the earth the gravity decreases hence weight decreases.
