We propose a well-balanced scheme for the modified Lifshitz-Slyozov equation, that incorporates a size-diffusion term. The method uses the Fokker-Planck structure of the equation. In turn, large time simulations can be performed with a reduced computational cost, since the time step constraints are relaxed. The simulations bring out the critical mass threshold and the relaxation to equilibrium, which can be expected from the formal analogies with the Becker-Döring system.