The study of the bremsstrahlung photon emission accompanying fragments produced in the spontaneous fission of heavy nuclei by a fully quantum approach is presented for the first time. This kind of problem requires the knowledge of wave functions of the fissioning system leading to a wide distribution of couples of fragments that are the products of fission. With the aim of obtaining these wave functions, the interaction potential between the emitted fragment and residual nucleus is calculated by a standard approach. A new procedure was performed that allows an increase in the accuracy of calculations of radial integrals in the far asymptotic region and the achievement of the convenient convergence in calculations of the spectra. The total probability of the emitted photons in the spontaneous fission of Cf252 was calculated in such a way. We obtained good agreement between theory and experimental data up to 38 MeV for the bremsstrahlung spectrum of photons while the calculation of the total probability of photon emission accompanying fragments was performed up to an energy of 60 MeV. The analysis of contributions in the bremsstrahlung spectrum accompanying the emission of light, medium, and heavy fragments in the fission of Cf252 is presented.