Let \(H\) and \(G\) be groups. A group homomorphism from \(H\) to \(G\) is called a localization if and only if it induces a bijection between \(\Hom(G,G)\) and \(\Hom(H,G)\). Following \textit{J. L. Rodríguez, J. Scherer} and \textit{J. Thévenaz} [Isr. J. Math. 131, 185-202 (2002; Zbl 1010.20007)] the authors study the equivalence relation that localization induces on the family of finite non-Abelian simple groups.