A new dispersion (asymptotic) theory is proposed for the peripheral sub-and abovebarrier charged particle transfer A(x, y)B reaction in the three-body (A, a and y) model where x = y + a and B = A + a, and a is a transferred particle. It is based on the combination of the dispersion theory and the conventional DWBA method. The explicit forms have been derived for the exact three-body pole amplitude and differential cross section in which the contribution of the three-body (A, a and y) Coulomb dynamics of the transfer mechanism in the peripheral partial amplitudes, corresponding to partial waves with l i >> 1, is taken into account correctly. For the specific peripheral proton and triton transfer reactions, the comparative analysis of the peripheral partial amplitudes at l i >> 1 , which correspond to the one-step pole and exact three-body pole amplitudes as well as those of the "post"-approximation and the post form of the conventional DWBA, is performed with each other. It shows the absolute inapplicability of the "post"-approximation usually applied for getting an information about specific asymptotic normalization coefficients being astrophysical interest.