The reaction of the isostructural anions of group 13 hydrides EH4- (E = B, Al, Ga) with proton donors of different strength (CH3OH, CF3CH2OH, and CF3OH) was studied with different theoretical methods [DFT/B3LYP and second-order Møller-Plesset (MP2) using the 6-311++G(d,p) basis set]. The results show the general mechanism of the reaction: the dihydrogen-bonded (DHB) adduct (EH...HO) formation leads through the activation barrier to the next concerted step of H2 elimination and alkoxo product formation. The structures, interaction energies (calculated by different approaches including the energy decomposition analysis), vibrational E-H modes, and electron-density distributions were analyzed for all of the DHB adducts. The transition state (TS) is the dihydrogen complex stabilized by a hydrogen bond with the anion [EH3(eta2-H2)...OR-]. The single exception is the reaction of BH4- with CF3OH exhibiting two TSs separated by a shallow minimum of the BH3(eta2-H2)...OR- intermediate. The structures and energies of all of the species were calculated, leading to the establishment of the potential energy profiles for the reaction. A comparison is made with the mechanism of the proton-transfer reaction to transition-metal hydrides. The solvent influence on the stability of all of the species along the reaction pathway was accounted for by means of polarizable conductor calculation model calculations in tetrahydrofuran (THF). Although in THF the DHB intermediates, the TSs, and the products are destabilized with respect to the separated reactants, the energy barriers for the proton transfer are only slightly affected by the solvent. The dependence of the energies of the DHB complexes, TSs, and products as well as the energy barriers for the H2 release on the central atom and the proton donor strength is also discussed.