The interference between the K+K- S-wave and P-wave amplitudes in B-s(0) -> J/psi K+K- decays with the K+K- pairs in the region around the phi(1020) resonance is used to determine the variation of the difference of the strong phase between these amplitudes as a function of K+K- invariant mass. Combined with the results from our CP asymmetry measurement in B-s(0) -> J/psi phi decays, we conclude that the B-s(0) mass eigenstate that is almost CP = +1 is lighter and decays faster than the mass eigenstate that is almost CP = -1. This determines the sign of the decay width difference Delta Gamma(s) = Gamma(L) - Gamma(H) to be positive. Our result also resolves the ambiguity in the past measurements of the CP violating phase phi(s) to be close to zero rather than phi. These conclusions are in agreement with the standard model expectations.