Herein, the effect of the initial copper content of co‐evaporated Cu(In1−x,Gax)Se2 (CIGS) absorber films on the impact of a post‐annealing step in elemental sulfur atmosphere is studied. The Cu concentration is varied over a wide range ([Cu]/[III] = CGI = 0.57–1.23), allowing to identify composition‐dependent trends in phase formation, chemical rearrangements, and solar cell performance after sulfurization. For all samples, a ternary CuInS2 layer forms at the surface. In addition, sulfur 1) is incorporated in randomly distributed CuIn(S,Se)2 mixed crystals underneath CuInS2; 2) diffuses into multidimensional defects (e.g., dislocations and grain boundaries); and 3) is bound in Na–In–S surface plates. It is found that Cu‐poor absorber composition (CGI ≤ 0.82) favors CuInS2 growth as compared with close‐stoichiometric CIGS films, driven by a faster diffusion of Cu toward the surface. For Cu‐rich absorbers (CGI > 1), Se—S exchange is significantly accelerated, presumably by the presence of Cu2−xSe phases reacting to Cu2−xS and eventually catalyzing CuInS2 formation. Finally, open‐circuit voltage (VOC), fill factor (FF), and efficiency (η) of corresponding solar cells increase after sulfurization with increasing CGI until stoichiometry is reached. The result is explained by a mitigated Cu depletion of the absorber bulk after sulfurization for close‐stoichiometric CIGS.