From THE HISTORY OF WINCHESTER FIREARMS, 1866-1980, 5th Ed., by Duncan Barnes;
page 12;
"Factory records indicate , however, that during later years occasional small lots of M/66 firearms were manufactured; the record of the last firearm assembled bears the date August 1898. In 1891 1,020 M/66 component parts, on hand for many years, were used in the assembly of rifles chambered for the 44 "Henry" center fire cartridge and shipped to a firm in Brazil. In making up this lot of guns it was necessary to change the breech pin by discarding the Breech Pin Snapper, substituting a center fire firing pin and also inserting a threaded bushing in the face of the breech pin base with a hole in the center to allow the point of the firing pin to protrude and hit the primer. All other components were the same as previously used on the standard M/66, 44 caliber rimfire rifles, except for the chambering of the barrel."
A perusal of my COTW,3d, shows that the cartridge dimensions of the 44 Henry Flat CF most closely match the .44 American, not the 44 Russian. Having said that, the most practical modern cartridge suitable for the 1866 would be the 44 Russian.
UBERTI, take note!