An accused gang member was sentenced to life in prison on Monday for his role in the 2010 killing of his girlfriend and her toddler son on New York's Long Island, federal authorities said.

Juan Elias "Cruzito" Garcia, 22, a reputed member of the murderous international gang known as MS-13, was convicted in March 2013 of murdering Vanessa Argueta, 19, and her son, Diego Torres, 2, the Office of the U.S. Attorney for the Eastern District of New York said in a press release.

Garcia and fellow gang members plotted the killing because they believed the young mother had disrespected the gang by sending rivals to attack Garcia, prosecutors said.

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In the execution-style shooting in Central Islip, New York, in February 2010, Argueta was shot in the chest and head and her son was shot twice in the head.

Garcia fled to El Salvador after the killing and remained a fugitive for four years. He was listed on the FBI's "Ten Most Wanted Fugitives," and soon afterward surrendered to authorities in Nicaragua and was returned to the U.S. for prosecution.

"Today's sentencing is the final chapter in the government's commitment to get justice for the victims," FBI Assistants Director-in-Charge Diego Rodriguez said in a statement. "Garcia and his fellow MS-13 members senselessly and callously murdered a young mother and her toddler five years ago."

After a lovers' quarrel, Garcia was threatened by rival gang members, who he said used information that he believed was provided by Argueta, the FBI said.

Garcia and two fellow gang members got permission from their leader to retaliate against the woman.

She and her son were lured into a wooded area, the FBI said. When the boy saw his mother killed, he started crying. He was hit by a bullet that knocked him down.

"Torres got back up and clutched onto Garcia's leg," when a second shot was fired, striking the boy in the head and killing him, the FBI said.

Fellow accused gang member Adalberto Ariel Guzman also was sentenced to life plus 35 years in prison after being convicted of charges related to the murders and accused gang member Rene Mendez Mejia is awaiting sentencing after pleading guilty to the murders.

Their reputed gang leader, Heriberto Martinez, has been sentenced to three life terms, plus 60 years, in prison for multiple convictions that include murder, racketeering and conspiracy, the FBI said.