Is it permissible to circumvent the Saudi embassy's condition regarding the age of the mahram, in order to perform Hajj with a son who is 14 years old, by presenting a false mahram to the embassy and a legitimate mahram before Allah?

The statement that a non-Mahram (definition) is a Mahram for a woman for Hajj is a forbidden lie. You should try to convince the embassy that the adult son is suitable as a Mahram, coupled with abundant supplication and piety towards Allah. "And whoever fears Allah – He will make for him a way out" and ease. If she is unable to obtain a Hajj visa with her son, she is excused, and lying is not obligatory for her. Although some jurists have permitted lying to attain a right that cannot be reached except through it, if her son is truly an adult and she cannot perform Hajj except by lying, we hope that she will not incur sin.