The video, which Cooper shared with multiple news outlets, shows the man moving back and forth from the area of floor he was working on to the hamper. At one point, he turns his back to the camera -- with a pair of underwear up to his face.
"You see him turn back around (and) put the underwear in the hamper, and before he does that, you see what looks like he is taking one last big breath in," Cooper told ABC7.
"I would have never imagined that somebody would do this," he told KTLA.
Cooper, who reported the incident to the moving company and filed a report with the Los Angeles Police Department, said one of the most disturbing aspects of the situation is that he was home, just feet away in the next room, when the incident took place.
KTLA reported that Cooper also called the repairman directly and told him what he had recorded. The man gasped when he learned of the video, Cooper said.
He seemed ready to apologize, but Cooper told him he wanted to hear nothing the man had to say.
"This gentleman violated a 5-year-old and 3-year-old's privacy, my family's privacy," Cooper said. "Obviously, my wife and I are really distraught over this and we want other people to know."
ABC7 reported that it is unclear if the man committed a crime, other than the theft of the underwear.
"From now (on) I can tell you that my wife and I will never let anybody else in this house without us standing by their side until they leave," Cooper told the news station.