The Kubo formula was used to derive a general expression for static electrical conductivity in a magnetic field directed parallel to the surface of a parabolic quantum well. Conditions for the applicability of the relaxation-time approximation for the calculation of the correlation functions were formulated using the cumulant-averaging method. The tensors of longitudinal and transverse conductivities in the dimensionally confined system under consideration, with allowance made for the interaction of electrons with acoustic and optical vibrations, were calculated. It is shown that the transverse conductivity in quantum-well systems is much higher (by several orders of magnitude) than in the bulk samples. The dependence of longitudinal conductivity on the magnetic field was studied for a highly degenerate electron gas.