Where are the solid points?

There are mirrors (retroreflectors) placed on the moon at specific locations. Many places around the world bounce a laser off of them to make measurements about the moon. They were placed the since the first moon landing. Your mom can go to one of the observatories that perform this study and verify the the laser measurement itself which is not possible to do without a mirror on the moon reflecting the laser back.

https://www.nasa.gov/feature/goddard/2020/laser-beams-reflected-between-earth-and-moon-boost-science