For a magnetized plasma, a reduction of the two-time formalism [V.~I.Erofeev, Journal of Plasma Physics 85, 905850104 (2019);V.~I. Erofeev, Contributions to Plasma Physics 62, e202100140 (2022)] to a highly informative scenario of redistribution of charged particles in momentum due to Coulomb collisions is reported. The consideration focuses on the standard case of an ideal classical ionized homogeneous plasma. It is found that the leading-order approximation of the scenario is consistent with the well-known generalizations of the Lenard--Balescu equation [A. Lenard, Ann. Phys. 10, 390--400 (1960); R. Balescu, Phys. Fluids 3, 52--63 (1960)] that take into account the leading magnetic field effect [N. Rostoker, Phys Fluids 3, 922-927 (1960); M.H.A. Hassan, C.J.H. Watson, Plasma Phys. 19, 237--247 (1977)]. A correction to the collision integral of this equation is developed that is due to time variations of plasma parameters.