To the best of my recollection Westley Richards patented "The Doll's Head", I believe it may date back into the 1860's..
Daniel Lefever did not patent "The Doll's Head". US Patent #205,193 was issued to D M Lefever of Syracuse NY on June 25, 1878. This patent included, among other features, Square Shoulders to the Doll's Head.
Barber & Lefever were in partnership from 1871 - 1874. Nichols & Lefever were in partnership from 1876 - 1879 so this patent was issued during the partnership with Nichols.
I cannot say if upon dissolving this partnership if John Nichols retained any rights to this patent or not. The rib extension on the gun in question does look virtually identical to Lefever's extension from that point on.
Some Parker's did use a square shoulder doll's head but it had a different configuration to Lefever's. I have read in the past they had to pay Lefever royalty for its use. This would seem highly unlikely if they had purchased the patent from John Nichols.


Miller/TN
I Didn't Say Everything I Said, Yogi Berra