  V. Bergelson and N. Hindman proved that IP$^{\star}$- sets contain all
possible finite sums and products of a sum subsystem of any sequence in
$\mathbb{N}$. In a recent work the second author of this article has proved
that a stronger result holds for dynamical IP$^{\star}$- sets. In this article
we will establish a non-commutative version of this result. We will prove that
a richer configuration is contained in dynamical IP$^{\star}$- sets in weak
rings.
