For a magnetized plasma, a reduction of the two-time formalism (Erofeev 2019 J. Plasma Phys.85 905850104, Erofeev 2022 Contrib. Plasma Phys.62 e202100140) 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 (Lenard 1960 Ann. Phys.10 390–400, Balescu 1960 Phys. Fluids3 52–63) that take into account the leading magnetic field effect (Rostoker 1960 Phys. Fluids3 922–7, Hassan and Watson 1977 Plasma Phys.19 237–47). A correction to the collision integral of this equation is developed that is due to time variations of plasma parameters.