Here in White Plains, a break in the case came on Tuesday when a friend of Ms. Duplaga’s sent her a congratulatory text message on the return of her stolen computer. “She said, ‘I don’t know what you’re talking about,’ and her friend said, ‘Well, you popped up as being online,’ ” Mr. Jackson said.

He said that Ms. Duplaga immediately signed on to another Macintosh computer and, using a feature called “Back to My Mac,” was able to gain access to her missing laptop remotely. She could see that that the person who had her computer was shopping for beds, Mr. Jackson said. Then it occurred to her that she could activate a camera on her laptop and watch the thief live.