This article presents an exact solution for a perfect conversion of a TM-polarized surface wave (SW) into a TM-polarized leaky wave (LW) using a reciprocal and lossless penetrable metasurface (MTS) characterized by a scalar sheet impedance, located on a grounded slab. On contrary to the known realizations of LW antennas, the optimal surface reactance modulation which is found here ensures the absence of evanescent higher-order modes of the field Floquet-wave expansion near the radiating surface. Thus, all the energy carried by the SW is used for launching the single inhomogeneous plane wave into space without accumulation of reactive energy in the higher-order modes. It is shown that the resulting penetrable MTS exhibits variation from an inductive to a capacitive reactance passing through a resonance. The present formulation complements a previous article of the authors, in which a perfect conversion from TM-polarized SW to TE-polarized LW was found for impenetrable boundary conditions. Here, the solution takes into account the grounded slab dispersion, and it is convenient for practical implementation.