That's called IMD (In-mold-decoration). There is a new version now where the mold grabs the film a heater is inserted between the two halves of the mold to heat the film, film is vacuum formed to one half of the mold cavity, then the resin is injected. The image from the film is transferral to the molded part.What they used was much more simple. A reel of film on one side of the mold, and a take up reel on the other side. When the mold opened the takeup reel advanced the film. The "good" side of the film faced the finished side of the mold cavity and the injected plastic forced it against the cavity. Crude but did the job needed.