That is probably the Robert W. Woodruff CHE-Grade .410-bore. See pages 650 and 651 of
The Parker Story. It was a gift to the Cody Firearms Museum from Woodruff's friend and business associate Joseph W. Jones. It has been one of my regular stops when the Remington Society of America has done their annual seminars at The Buffalo Bill Center of the West, 2003 and 2014. I counted over 100 Parker Bros. guns on display there.