Reversible diffusion-influenced pseudo first order reaction A+B reversible arrow C with static particles in excess is rigorously studied. Under most general assumptions, the problem of the reversible reaction kinetics is reduced to the consideration of the effective irreversible reaction studied by conventional methods. In the framework of the average t-matrix approximation (ATA) we reproduce some results derived earlier and establish their applicability limits. Rigorous investigation of the kinetics behavior at long times shows that the t(-3/2) law predicted earlier and reproduced by ATA has a different concentration-dependent amplitude. On the basis of diagrammatic summation, providing correct long-time asymptotics, a modified theory has been developed. The range of validity of the modified theory is much wider than that of ATA and similar theories.