Moon Lander: How We Developed the Apollo Lunar Module (Smithsonian History of Aviation and Spaceflight (Paperback))

Cause at that time faking it would have been much more harder than doing the actual thing. To fake it consistensly through the tons of reports, recordings and pictures would have been quite impossible. If you are interested in the technical details there are tons of books available written by key persons from the Apollo program like Chris Kraft, of course Gene Kranz, and a lot of Apollo Astronauts. Thomas Kelly, the Chief Designer of the Lunar Module buildt by Grumman has also written a masterpiece: https://www.amazon.com/Moon-Lander-Developed-Smithsonian-Spaceflight/dp/1588342735 For a thoroughly technical overview I recommend this one: https://link.springer.com/book/10.1007/978-1-4419-7179-1