In a previous paper (I), we have derived a rigorous series expression for the superconducting critical temperature Tc. Here we discuss the region of convergence of this series, and the possibility of its extension through analytical continuation. Our conclusion is that the above mentioned series or its analytical extension is convergent within the whole region ∞ >λ>λ0. By λ0 we mean the smallest value of λ which can be taken such that the equation determining Tc in the Matsubara representation has a real positive solution. It is in fact the Coulomb pseudopotential. Therefore, ex-cluding possibly a few very weakly coupled ones, our Tc formula is applicable to all superconductors.