The decays of Bs0 and B¯¯¯¯0sB¯s0 mesons into the J/ψK+K− final state are studied in the K+K− mass region above the ϕ(1020) meson in order to determine the resonant substructure and measure the CP-violating phase, ϕs, the decay width, Γs, and the width difference between light and heavy mass eigenstates, ΔΓs. A decay-time dependent amplitude analysis is employed. The data sample corresponds to an integrated luminosity of 3 fb−1 produced in 7 and 8 TeV pp collisions at the LHC, collected by the LHCb experiment. The measurement determines ϕs = 119 ± 107 ± 34 mrad. A combination with previous LHCb measurements using similar decays into the J/ψπ+π− and J/ψϕ(1020) final states gives ϕs = 1 ± 37 mrad, consistent with the Standard Model prediction.