It is interesting that I have written about this in my new book Sir John Moore and the Universal Soldier. My understanding is that Rottenburg wrote the book for his 5/60th in German and it was this that was translated. Sir John Moore translated Rottenburg plus Johann Ewald in his instruction to Irish Militia Light Infantry dated early 1798. The Fawcett translation is August 1798. There are a number of funbdamental differences in translation. The latter had influenced Rottenburg.
The book explores the influences on Moore and the instruction of Light Infantry under the Shorncliffe System of Training.