I inherited a picture from my grandfather of then-Colonel Irwin Rommel when he was visiting the United States in 1937/38 to study the cavalry tactics of the Civil War. From what my grandfather could remember, Rommel concentrated on Forrest, Morgan, Wheeler, and Stewart.
At the time, my grandfather was a sergeant in the Mississippi National Guard (he later accepted a commission in the regular Army) and his horse-drawn artillery was conducting maneuvers with some other horse units in Western Tennessee and Rommel and several other German officers were observers during these maneuvers.
Years later, in the early 1950's, my grandfather commanded an ACR battalion on the East-West German border and became good friends with a German officer who had been Rommel's aide during that study tour and he gave my grandfather the picture to remember the event.
You say the photo was actually taken during the visit to the U.S.?
my grandfather commanded an ACR battalion
ACR = ?
There is a novel "Rommel and the Rebel" by Lawrence Wells. The plot is based on the idea that one of Montgomery's intelligence officers enlists the help of a Southern historian, who is an expert on N.B. Forrest, to help predict Rommel's moves in the desert, based on "What would Forrest do?" Not great literature, but fairly good reading.
You might want to check your grandfather's story. Rommel wasn't a cavalry officer and he never visited the U.S. His career prior to WWII was with mountain troops, and the book that he was known for was actually on infantry tactics. He had nothing to to with mounted or motorized units until 1940.