Cops on Saturday busted the man they say fatally shot a Queens mom in the neck as she stood at her children’s bedroom window this week — and the cast on his left leg was a key clue to his identity.

Issam Elabbar, 31, of Queens, has been charged with murder for the senseless death of Bertha Arriaga, 43, a mother of three, according to cops.

Investigators caught Elabbar 68 hours after the shooting, through “an exhaustive search of video” from the scene and beyond, Deputy Chief Julie Morrill of the NYPD’s Detective Bureau Queens North told reporters.

“The unique appearance of a cast on his left leg gave our detectives an additional lead,” she said.

Investigators believe Elabbar intentionally fired up at the Jackson Heights building because people inside were yelling down at him as he and another man made a commotion while trying to steal a motorized scooter, sources told The Post.

“He fired up at the building to scare the people to go back inside,” one said. “To get them to leave him alone.”

A neighbor has described men making noise on the street before the gun fired at around 12:45 a.m.

Video showed Elabbar firing a single shot up at the building without looking to see where it would strike, prosecutors said.

“At this time, the shot appears to have been fired in the direction of the building, and I can’t say it was intentionally fired at the building,” Morrill said.

Arriaga, 43, left behind three sons.

The eldest, Angel, 14, is the one who rushed into the bedroom when the shot rang out.

He found her bleeding on the floor of their 34th Avenue apartment, a relative said previously. She had been shot once through the neck.

The other boys are Victor, 10, and George, 6.

The arrest “brings some relief to the family,” but it doesn’t change that Arriaga “is gone,” her brother-in-law, Javier Aguilar, 42, told The Post later Saturday.

Aguilar thanked the detectives for making an arrest.

Still, the family remains furious that “for just a mistake,” —  because of a shot apparently carelessly fired — his brother is now a widower and his three nephews are without a mother.

Added Aguilar: “My brother, he doesn’t feel better… We have to continue with our funeral arrangement. That’s all I can say.”

Elabbar said nothing as he was rolled out of the 115th Precinct in Jackson Heights in a wheelchair Saturday morning.

He ignored a Post reporter’s shouted questions about the deadly shooting.

The Corona man’s left lower leg was in a cast from a previous injury, cops said Saturday.

Cops had taken him to Elmhurst Hospital when he complained of leg pain after he was brought in for questioning on Friday night.

He was being returned from the precinct to the hospital Saturday for further treatment, police said.

He has been charged with murder, manslaughter, criminal possession of a weapon, and petit larceny.

Officials in both the NYPD and Queens DA’s office called the shooting heartbreaking.

“A youngster, just 14 years old, woke to the sounds of his mother gasping for air and found her bleeding and near death,”  Queens DA Melinda Katz said after the arrest.

“Because of the defendant’s depraved indifference, a husband is now without a wife and three children are now without a mom. How senseless.”

Elabbar faces up to 25 years-to-life in prison if convicted.

Additional reporting by Sara Dorn and Laura Italiano