I doubt there would be any recordings of him speaking English though he was certainly fluent and spent several years in the US.He was actually fascinated by the America he saw a good portion of the country in his spare time and he also had an understanding of the industrial capacity of the US and an understanding of American resolve.
The reason I doubt that there are any recordings is because in Japan in the years leading up to WWII(an during of course) there was a lot of propaganda to be anti western that the Japanese cloud do anything that a westerner could do better so a major military leader would not be keen on being recorded speaking English.Not surprisingly the inverse propaganda occurred in the US.
I have no doubt that Yamamoto had many in depth conversations with his American counterparts during his tenure in the US.Of course what was said would always be guarded because both Japanese and American military thinkers knew that sooner or later the nations would confront each other.
What is less well known is that many US navy naval officers did stints as naval attaches in Japan in the 20's to mid 30's their underlying goal was to learn Japanese so that they could later help with code breaking the Japanese did not have this foresight and only the wiser officer such as Yamamoto expanded their knowledge while serving as an attache.
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