A form of Ryōi Shintō-ryū Jūjutsu was taught to U.S. Military during WW1 & WW2

In the a research paper entitled:
‘The diffusion routes of Jiu-Jitsu to and in the U.S. since the turn of the last century to 1930s:Focus on the transfiguration and succession of Jiu-Jitsu by the two Americans’

Yabu Kotaro (2012) (Ritsumeikan University, Japan) states that John J. O’Brien studied JigoTenshin-ryū Jūjutsu (自剛天真流柔術) in the Nagasaki foreign settlement and then returned to the U.S.A..

Jigō Tenshin-ryū Jūjutsu (自剛天真流柔術), aka Ise Jitoku Tenshin-ryū (為勢自得天眞流) is an off-shoot of the main Kasahara (笠原) line of the Ryōi Shintō-ryū Jūjutsu (良移心当流柔術).

In a further article entitled ‘ A Beginning History of Old School Jujutsu - Part 1’ by Carl Cestari (2003) published online: on boxingscene.com
Cestari states that John J. O’Brien taught Captain Anthony Joseph Drexel Biddle Sr. (1874–1948), who taught hand-to-hand combat to U.S. troops during the First and Second World Wars.

Here are some illustrations from Biddle’s book ‘Do or Die’ (published 1944).