When should you use par vs. à? When you describe the agent with a clause introduced by que(that), the agent is introduced by the preposition à instead of par.
J’ai fait croire à mes amis que j’étais encore au cinéma !
I made my friends believe that I was still at the movie theater!
Just don’t forget, any time you are using both a receiver and an agent after the causative verb, the agent is marked by a preposition! This is different from sentences that only have a receiver, where the preposition is not needed.