While picking up 4 ½” liner from catwalk to the mouse hole using driller side air winch. The Floorman was having difficulties in latching the elevator to the liner in the mouse hole. While his hands were still holding the handles of the elevator, he gave a verbal signal to the Driller to operate the link tilt backwards slightly. When the bails tilted back, the elevator moved downwards and struck the Floorman' s finger resulting in a crush injury to his right hand middle finger.