Strauss had published his piece on Machiavelli’s Prince in 1957 and not long thereafter it appears that Carl Schmitt read it….
…and in a letter to Reinhart Koselleck, Schmitt appears to relish the possibility of a rebuttal of Strauss by George Schwab (https://ncafp.org/team/dr-george-d-schwab/)
In Sam Zeitlin’s translation of Schmitt’s Dialogues on Power & Space, Sam provides a few notes regarding these formulations.