In looking at the muster roll for Company H, 22d PA Cavalry from Dr. S. P. Bates' "History of the PA Volunteers, 1861-1865," I see a Jacob Johnson listed:

Jacob Johnson
Saddler
Mustered In: February 29, 1864
Mustered out with Company H, 3d Regiment Provisional Cavalry, October 31, 1865.

The 3rd PA Provisional Cavalry was organized at Cumberland, Md., June 24, 1865, by consolidation of 18th and 22nd Pennsylvania Cavalry. Duty at Clarksburg, W. Va., till October, 1865. Mustered out October 31, 1865.

The muster roll poster you described sounds like the muster rolls prepared by the GAR following the war. I have a similiar one for my g-grandfather's company and regiment (Company B, 211th PA Volunteers).

Alice J. Gayley
Pennsylvania in the Civil War
http://www.pa-roots.com/~pacw/