Extremely Loud and Incredibly Close

Nine-year-old Oskar Schell (Thomas Horn), who suffers from Asperger syndrome, is the son of German American Thomas Schell (Tom Hanks).[5] Thomas would often send Oskar on missions to do something involving one of his riddles. The last riddle he ever gives Oskar is proof that New York City once possessed a Sixth Borough. In a flashback, Thomas and Oskar play a scavenger hunt to find objects throughout New York City. The game requires communication with other people and is not easy for the socially awkward Oskar who is told "If things were easy to find, they wouldn't be worth finding".
On September 11, 2001, Oskar and his classmates are sent home from school early while his mother Linda (Sandra Bullock) is at work. When Oskar gets home, he finds five messages from his father on the answering machine saying he is in the World Trade Center. When Thomas calls for the sixth time, although Oskar is present to answer this call, he is too scared to answer. The machine records a sixth message which stops when the building collapses. Oskar knows his father has been killed and falls to the floor. He replaces the answering machine with a new one and hides the old one so his mother will never find out.
A few weeks after what Oskar calls "the worst day," he confides in his German grandmother and they become closer. Oskar's relationship with his mother worsens since she cannot explain why the World Trade Center was attacked and why his father died. Oskar tells his mother he wishes it had been her in the building, not his father, and she responds, "So do I". After, Oskar says he did not mean it, but his mother doesn't believe him.
A year later, Oskar finds a vase in his father's closet with a key in an envelope with the word "Black" on it. He vows to find what the key fits. He finds 472 Blacks in the New York phone book and plans to meet each of them to see if they knew his father. He first meets Abby Black (Viola Davis), who has recently divorced her husband. She tells Oskar she did not know his father.
One day, Oskar realizes that a strange man (Max von Sydow) has moved in with his grandmother. This stranger does not talk because of a childhood trauma caused by his parents' death in World War II. He communicates with written notes and with his hands which have "yes" and "no" tattooed on them. As they become friends and go together on the hunt to find what the key fits, Oskar learns to face his fears, such as those of public transport and bridges. Eventually, Oskar concludes that the stranger is his grandfather and plays the answering machine messages for this stranger. Before playing the last message, the stranger cannot bear listening any longer, this message being his son's last words, and stops Oskar. Later on, the stranger moves out and tells Oskar not to search anymore.
When Oskar looks at a newspaper clipping his father gave him, he finds a circled phone number with a reference to an estate sale. He dials the number and reaches Abby, who wants to take Oskar to her ex-husband, William, who may know about the key. William (Jeffrey Wright) tells Oskar he has been looking for the key. William had sold the vase to Oskar's father who never knew the key was in the vase. The key fits a safe deposit box where William's father left something for him. Disappointed and distraught because the key does not belong to him, Oskar confesses to William that he did not pick up the phone during his father's sixth and final phone call and then goes home.
Oskar's mother tells Oskar she knew he was contacting the Blacks. She then informs him that she visited each Black in advance and informed them that Oskar was going to visit and why. Oskar makes an artbook-like scrapbook filled with pop-ups and pull tabs like a children's book, of his scavenger hunt and all the people he met and titles it "Extremely Loud and Incredibly Close." At the end of the book there is a pull tab, showing an animation in which Thomas's body is falling up instead of down.
Oskar's grandfather returns to live with Oskar's grandmother.

Question: Who did Wilson sell the vase to?
Answer: William sold the vase to Oskars father.