The formalism to describe heavy-ion double charge exchange (DCE) processes in the eikonal and small-momentum transfer approximations introduced in Phys. Rev. C 98, 061601(R) (2018) is briefly discussed. It is also shown that, under the previous approximations, the heavy-ion DCE cross-section can be factorized in terms of a reaction and a nuclear part. A double charge exchange effective potential is explicitly derived in the closure approximation and also for the first time the explicit form of the DCE nuclear matrix elements, that are of the form of double Gamow-Teller and double Fermi. The recent hypothesis of a linear correlation between double Gamow-Teller neutrinoless double beta decay and DCE nuclear matrix elements is confirmed thanks to the first explicit derivation of DCE nuclear matrix elements, and by means of microscopic IBM2 calculations.