Dielectric and infrared spectroscopies were employed to study inter- and intramolecular glass-transition dynamics in the series of hyperbranched polyesters of the second, third, and fourth generations. Our study shows that conductivity relaxation becomes increasingly faster than structural relaxation as the glass transition temperature Tg is approached, signifying decoupling between translational motions of charges and reorientation of molecules. Depending on the polymer’s generation conductivity relaxation times can be up to few orders of magnitude faster than structural dynamics. Because of extensive hydrogen bonding network, the most significant contribution to the total ionic conductivity comes from proton transfer along hydrogen bonds. Decoupling phenomenon was accompanied by narrowing the dispersion of the conductivity relaxation with decreasing temperature that reaches almost exponential decay in the glassy state. Finally, by analyzing the absorption spectra in terms of integral intensity, we have demonstrated significant role of H-bonded moieties in the course of vitrification of investigated materials.