The branching fraction of the decay B+→ψ(2S)ϕ(1020)K+, relative to the topologically similar decay B+→J/ψϕ(1020)K+, is measured using proton-proton collision data collected by the LHCb experiment at center-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9fb−1. The ratio is found to be 0.061±0.004±0.009, where the first uncertainty is statistical and the second systematic. Using the world-average branching fraction for B+→J/ψϕ(1020)K+, the branching fraction for the decay B+→ψ(2S)ϕ(1020)K+ is found to be (3.0±0.2±0.5±0.2)×10−6, where the first uncertainty is statistical, the second systematic, and the third is due to the branching fraction of the normalization channel.The branching fraction of the decay B+→ψ(2S)ϕ(1020)K+, relative to the topologically similar decay B+→J/ψϕ(1020)K+, is measured using proton-proton collision data collected by the LHCb experiment at center-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9fb−1. The ratio is found to be 0.061±0.004±0.009, where the first uncertainty is statistical and the second systematic. Using the world-average branching fraction for B+→J/ψϕ(1020)K+, the branching fraction for the decay B+→ψ(2S)ϕ(1020)K+ is found to be (3.0±0.2±0.5±0.2)×10−6, where the first uncertainty is statistical, the second systematic, and the third is due to the branching fraction of the normalization channel.The branching fraction of the decay B+→ψ(2S)ϕ(1020)K+, relative to the topologically similar decay B+→J/ψϕ(1020)K+, is measured using proton-proton collision data collected by the LHCb experiment at center-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9fb−1. The ratio is found to be 0.061±0.004±0.009, where the first uncertainty is statistical and the second systematic. Using the world-average branching fraction for B+→J/ψϕ(1020)K+, the branching fraction for the decay B+→ψ(2S)ϕ(1020)K+ is found to be (3.0±0.2±0.5±0.2)×10−6, where the first uncertainty is statistical, the second systematic, and the third is due to the branching fraction of the normalization channel