Synopsis We consider theoretically the process of dielectronic recombination (DR) with H-like ions where two-electron one-photon (TEOP) transitions take place. We focus our attention on the channel with transitions to the ground state of the He-like ions and emission of K_{α α} photon. Total and differential cross sections of DR with TEOP are calculated for wide range of H-like ions: from B⁴⁺ to Xe⁵³⁺. The resonant Fano-like structure of the cross section is observed. The resonant energies, widths and TEOP transition probabilities are calculated.