Existence of a map $\phi:\mathbb{Z}_{N^2}^* \mapsto \mathbb{F} $

Question

Is there a map between the group of $\mathbb{Z}_{N^2}^*$ where $N$ is a composite number , a product of two equal size secure prime numbers $p$ and $q$ and a finite field $\mathbb{F}$, such that for all $x \in \mathbb{Z}_{N^2}^*$ there is a polynomial representation of $x \in \mathbb{F}$ ?