A New Relation Between Lerch's $\Phi$ and the Hurwitz Zeta

A new relation between the Lerch's transcendent, $\Phi$, and the Hurwitz zeta, $\zeta(k,b)$, at the positive integers is introduced. It is derived simply by inverting the relation presented in the precursor paper with one of two approaches (its generating function or the binomial theorem). This enables one to go from Lerch as a function of Hurwitz zetas (of different orders), to Hurwitz as a function of Lerch. A special case of this new functional equation is a relation between the Riemann's zeta function and the polylogarithm