Henry Hill says, "As far back as I can remember, I always wanted to be a gangster", referring to his idolization of gangsters in his 1950s blue-collar, predominantly Italian-American neighborhood in East New York, Brooklyn. Wanting to be part of something significant, Henry quits school and goes to work for them. He is able to make a living for himself and learns the two most important lessons in life: "Never rat on your friends, and always keep your mouth shut", the advice given to him after being acquitted of criminal charges early in his career.
Henry is taken under the wing of local mob leader, Paul "Paulie" Cicero and his associates: James "Jimmy the Gent" Conway, who loves hijacking trucks; and Tommy DeVito, an aggressive armed robber with a temper. In late 1967, they commit the Air France Robbery. Enjoying the perks of their criminal life, they spend most of their nights at the Copacabana carousing with women. Henry meets and later marries Karen, a Jewish woman from the Five Towns area of Long Island. Karen is initially troubled by Henry's criminal activities but is soon seduced by his glamorous lifestyle.
On June 11, 1970, Billy Batts, a mobster in the Gambino Crime Family, insults Tommy about being a shoeshine boy in his younger days. Enraged, Tommy and Jimmy attack and kill him. Knowing their murder of a made member would mean retribution from the Gambino crime family, which could possibly include Paulie himself being ordered to kill them, Jimmy, Henry, and Tommy cover up the murder. They transport the body in the trunk of Henry's car and bury it upstate. Six months later, Jimmy learns the burial site will be developed, forcing them to exhume the decomposing corpse and move it.
Henry sets up his mistress, Janice Rossi, in an apartment. When Karen finds out about their relationship, she tries to confront Janice at the apartment building and then threatens Henry at gunpoint at home. Henry goes to live in the apartment with Janice, but Paulie mediates and directs him to return to Karen after completing a job for him; Henry and Jimmy are sent to collect from an indebted gambler in Florida. However, they are arrested after being turned in by the gambler's sister, a typist for the FBI. Jimmy and Henry receive ten-year prison sentences.
In prison, Henry sells drugs smuggled in by Karen to support his family on the outside. After his early release in 1978, Henry further establishes himself in the drug trade, ignoring Paulie's ban on drug trafficking, and convinces Tommy and Jimmy to join him. Jimmy and a lot of Henry's associates commit the Lufthansa heist at John F. Kennedy International Airport, stealing $6 million. However, after a few members buy expensive items and the getaway car is found by police, Jimmy has most of the crew killed. Tommy is eventually killed in retribution for Batts' murder, having been fooled into thinking he would become a made man.
By May 11, 1980, Henry is a nervous wreck from cocaine use and insomnia. He tries to organize a drug deal with his associates in Pittsburgh, however he is arrested by narcotics agents and jailed. After being bailed out, Karen tells him she flushed $60,000 worth of cocaine down the toilet to prevent FBI agents from finding it during their raid, leaving the family virtually penniless. Feeling betrayed by Henry's dealing drugs, Paulie gives him $3,200 and ends any association with him. Facing federal charges, and realizing Jimmy plans to have him killed, Henry decides to enroll in the Witness Protection Program. He gives sufficient testimony to have Paulie and Jimmy arrested and convicted. Forced out of his gangster life, Henry now has to face living in the real world. He narrates: "I'm an average nobody. I get to live the rest of my life like a schnook".
Subtitles explain that Henry was subsequently arrested on drug charges in Seattle, Washington, but has been clean since 1987. He and Karen separated in 1989 after twenty five years of marriage. Paul Cicero died in Fort Worth Federal Prison of respiratory illness in 1988 at age 73. Jimmy, in 1990, was serving a twenty-year-to-life sentence in a New York State prison.

Question: Who turns in Henry and Jimmy?
Answer: the gambler's sister
Alternative answer: The gambler's sister