A method for the calculation of transition amplitudes of two-photon ionization processes is developed. It is based on computing a correlation function, which enables the summation over intermediate states of two-photon transitions. Two-photon ionization transition amplitudes were calculated in the lowest order of perturbation theory with taking into account many-electron correlations. The noniterative numerical scheme provided a solution of the differential equation for the correlation function at exciting-photon energies close to the intermediate discrete resonance states. Cross section and angular distribution parameters for photoelectrons of the two-photon 3p photoionization of Ar were calculated. The exciting-photon energy ranged from 8 eV to 15 eV. For the first time an ab initio polarization potential considers the polarization of the atomic core by the excited photoelectron was included in the calculation. This effect increases the photoionization cross section at the photon energy from 8 eV to 10 eV by approximately 15% and shifts the computed energies of the intermediate discrete-state resonances, bringing them to excellent agreement with the experimental energies.