  In this paper, we will show that if two meromorphic mappings $f$ and $g$ of
$\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ have the same inverse images for
$(2n+2)$ moving hyperplanes $\{a_i\}_{i=1}^{2n+2}$ with multiplicities counted
to level $l_0$ then the map $f\times g$ must be algebraically degenerated over
the field $\mathcal R\{a_i\}_{i=1}^{2n+2}$, where $l_0=3n^3(n+1)q(q-2)$ with
$q=\binom{2n+2}{n+2}$. Our result generalizes the previous result for fixed
hyperplanes case of Fujimoto and also improves his result by giving an explicit
estimate for the number $l_0$.
