The codegree isomorphism problem for finite simple groups II

Let H be a nonabelian finite simple group. Huppert's conjecture asserts that if G is a finite group with the same set of complex character degrees as H, then $G\cong H\times A$ for some abelian group A. Over the past two decades, several specific cases of this conjecture have been addressed. Recently, attention has shifted to the analogous conjecture for character codegrees: if G has the same set of character codegrees as H, then $G\cong H$. Unfortunately, both problems have primarily been examined on a case-by-case basis. In this paper and the companion [15], we present a more unified approach to the codegree conjecture and confirm it for several families of simple groups.