Quasi-binary reaction of the deuteron breakup p + d → (pp) + n with the final proton–proton pair (pp) in the ¹S₀ state is analysed at initial energies 0.5–2 GeV in the kinematics of backward elastic pd-scattering pd → dp. On the basis of the main mechanisms of the pd → dp process, including initial and final state interactions, we show that unpolarized cross section and spin observables of this reaction exhibit important properties of the half-off-shell pp(¹S₀)-scattering amplitude, which are relevant to the nucleon–nucleon interaction at short distances.