Police said Marques Hoskins, 21, broke into the woman's West 21st Street apartment around 2:30 a.m. Sunday while she was out walking her dog, and the victim returned to find Hoskins sitting on her bed with her laptop, the New York Post reported Tuesday.
Hoskins fled with the victim's wallet and cellphone, police said.
Police said Sgt. Samuel Panuccio sent a text message to the woman's cellphone about 2 hours later, posing as the victim. Hoskins responded and said he would return the phone for $500 and asked if the woman wanted to "hook up" with him.
Panuccio accepted the offer and invited Hoskins to an undisclosed location, where he found himself under arrest. The wallet and phone were returned to the victim, who identified Hoskins as the thief.
Hoskins was arrested on burglary and related charges.