Is it permissible for a father to eavesdrop on his son's phone calls to uncover mysterious matters, especially since the son lies and conceals the truth?

It is not permissible to spy on one's child or on any Muslim, nor to pry into their private affairs, except in limited cases to achieve a benefit or avert a harm that cannot be realized except through spying. If a parent observes suspicious behavior from their child and fears for them, and finds no means to rectify them except by knowing what is hidden of their condition, then it is permissible for them to spy on the child within the bounds of necessity.