According to the Boston Globe, three men emerged from the darkness on a New Jersey side street Tuesday night, he said, screaming “terrorists’’ at the young couple out for a stroll with their toddler. They killed his young wife with a bullet in the heart and shot him, too, once in the shoulder and once in the ankle. But yesterday Kashif Parvaiz admitted to police that his story was a lie. Police investigating the execution-style killing of Nazish Noorani, 27, in the small town of Boonton, N.J., 30 miles from Manhattan, said yesterday that he was carrying out a plot to kill his wife, with the help of a Billerica woman, in a crime eerily reminiscent of the infamous Charles Stuart murder case that rocked Boston more than two decades ago. Parvaiz, who had been living in East Boston, was charged yesterday with the murder of his wife in a conspiracy with Antionette Stephen, 26, of Billerica.