  Let $\Gamma$ and $\Lambda$ be artin algebras such that $\Gamma$ is a
split-by-nilpotent extension of $\Lambda$ by a two sided ideal $I$ of $\Gamma.$
Consider the so-called change of rings functors
$G:={}_\Gamma\Gamma_\Lambda\otimes_\Lambda -$ and $F:={}_\Lambda
\Lambda_\Gamma\otimes_\Gamma -.$ In this paper, we find the necessary and
sufficient conditions under which a stratifying system $(\Theta,\leq)$ in
$\modu\Lambda$ can be lifted to a stratifying system $(G\Theta,\leq)$ in
$\modu\,(\Gamma).$ Furthermore, by using the functors $F$ and $G,$ we study the
relationship between their filtered categories of modules and some connections
with their corresponding standardly stratified algebras are stated. Finally, a
sufficient condition is given for stratifying systems in $\modu\,(\Gamma)$ in
such a way that they can be restricted, through the functor $F,$ to stratifying
systems in $\modu\,(\Lambda).$
