I just did a little checking, and while I couldn’t find anything about Rommel in the US, I did find out that in 1938, while an instructor at Potsdam, he started writing a book on armored cavalry and tank tactics that was intended as a sequel to his book on infantry tactics.
From what I've read Rommel's sequel was a project he started much later, during or shortly after the African campaign. He died before he could get very far. He could hardly have written it any earlier than that since prior to 1939 there weren't any proven tank tactics to write about, and Rommel himself didn't participate in developing them or command armored units until 1940.