[en] The first theoretical study of the effect of the final-state interaction on the initial core-hole lifetime is presented. The 4s-hole lifetime width of Sn metal is calculated by an ab-initio atomic many-body theory (Green's function method). When the final-state interaction in the 4p4d two-hole state, created by the 4s^-1-4p^-14d^-1 εf super Coster-Kronig (CK) transition of the initial 4s hole, is explicitly taken into account, the ab-initio atomic many-body calculation of the 4s-hole X-ray photoelectron spectroscopy (XPS) spectrum of Sn atom can provide excellent agreement with experiment in both the 4s-hole energy and the 4s-hole lifetime width. Otherwise, the many-body calculation underestimates considerably the 4s-hole lifetime width. The 4p4d two-hole state interacts strongly with the 4d triple-hole state by the 4p^-14d^-1-4d^-3 εf super CK transition. The interaction affects greatly the initial 4s-hole lifetime width