The previous matrix-theoretical analysis of the time lags and mean first passage times for reaction-diffusion transport in the Laplace domain [J. Chem. Phys. 106, 8022 (1997)] has been extended to the problems of membrane permeation, absorption and desorption. A matrix transport equation has been derived to calculate the flux (in the Laplace domain) for specified initial and boundary conditions corresponding to membrane permeation, absorption or desorption. Seven equality relations between fluxes for reaction-free diffusion and one for diffusion accompanying reaction have been found. Among them are two new equality relations which have been discovered by this matrix analysis. (C) 1997 American Institute of Physics.