A recursive function coding number theoretic functions

We show that there exists a fixed recursive function $e$ such that for all functions $h\text{\hspace{0.17em}⁣}:\mathbb{N}\to \mathbb{N}$, there exists an injective function $c_h\text{\hspace{0.17em}⁣}:\mathbb{N}\to \mathbb{N}$ such that $c_h(h(n))=e(c_h(n))$, i.e., $h=c_h^{-1}e{c}_h$.