The Count of Monte Cristo

In 1815, Edmond DantÃ©s, Second Mate of a French merchant vessel, and his friend Fernand Mondego, representative of the shipping company, seek medical help at Elba for their ailing captain. Napoleon Bonaparte, having kept his guardians from killing the pair, exchanges his physicianâs services with Edmond for the delivery of a letter to a Monsieur Clarion.
In Marseille, the company owner Morrell commends Edmond for his bravery, promoting him to captain over First Mate Danglars, who gave Edmond explicit orders not to land at Elba. Edmond states his intention to marry his girlfriend, MercÃ©dÃ¨s, whom Fernand lusts after.
Fernand and Danglars inform on Edmond, concerning the letter Fernand saw Napoleon hand him, to the cityâs Magistrate, Villefort, who has Edmond arrested. Villefort prepares to exonerate Edmond until he learns the letter is addressed to his father, a Bonapartist; he burns the letter and orders Edmond locked up in ChÃ¢teau d'If. Edmond escapes, and turns to Fernand for help, but Fernand holds him up and turns him over to the pursuing gendarmes. Edmond is consigned to the island prison and its sadistic warden, Armand Dorleac. Villefort has Fernand assassinate his father in exchange for persuading MercÃ©dÃ¨s that Edmond has been executed for treason and that she should take comfort in Fernand.
Six years later, Edmond is startled in his cell by an eruption in the ground; another prisoner, AbbÃ© Faria, has dug an escape tunnel. For seven years Faria educates Edmond in all facets of scholarship, including swordplay, in exchange for his help in digging a new escape route. Faria dies in a tunnel cave-in; before expiring he reveals a map to a treasure that Napoleon had imprisoned him for when he refused to produce it. Edmond escapes by switching himself for the priestâs body in the body bag, and is thrown into the sea, pulling Dorleac along with him, whom he drowns.
Edmond encounters a band of pirates preparing to execute a fellow, Jacopo; their leader, Luigi Vampa, decides justice, and entertainment also, would be better served by pitting Edmond and Jacopo in a knife fight. Edmond wins, but spares Jacopo, who swears himself Edmondâs man, and Edmond works for the pirates until they arrive in Marseille.
Edmond learns from Morrell, who does not recognize him, that Fernand and Danglars are complicit in his betrayal, and that Fernand and MercÃ©dÃ¨s have wed. With Jacopo, he locates Faria's treasure, and establishes himself as a Count in Parisian society.
Edmond ingratiates himself to the Mondegos by staging a kidnapping and rescue of their son, Albert. He lures Fernand, Villefort and Danglars into a trap by letting slip the notion that he has located the treasure, and is shipping it through Marseille; Danglars is caught red-handed, Villefort is arrested upon confessing that he ordered the hit on his father, but Fernand escapes.
MercÃ©dÃ¨s recognizes her former fiancÃ©. Eventually, she softens him, and they rekindle their relationship. As Fernand prepares to flee, she tells him that Albert is Edmondâs son.
Fernand encounters Edmond in the ruins of an estate where he hid what he thought were chests full of the treasure but contain nothing but dirt. Albert intervenes when Edmond attempts to kill Fernand, but MercÃ©dÃ¨s tells him of his true parentage. Fernand leaves, firing a shot that wounds MercÃ©dÃ¨s, and rides away, but changes his mind upon realizing that he has nothing left to live for; he rides back and calls Edmond out. The two fight to the death; Edmond prevails.
Edmond purchases ChÃ¢teau d'If, intending to raze it, but instead leaves it standing as he swears to the spirit of Faria to use his vast resources for nothing but good.

Question: How did Edmond ingratiate himself to the Mondegos?
Answer: Rescuing their son