The gravitational constant, G, is the same everywhere in the Universe.
Nno matter its earth or moon, its value is constant. ie 6.674 08 x 10-11 m3 kg-1 s-2
But the value of g changes.
The acceleration due to gravity on the surface of the Moon is about 1.625 m/s2, about 16.6% that on Earth's surface or 0.16 ɡ.[1]Over the entire surface, the variation in gravitational acceleration is about 0.0253 m/s2 (1.6% of the acceleration due to gravity). Because weight is directly dependent upon gravitational acceleration, things on the Moon will weigh only 16.6% of what they weigh on the Earth.