  Let $\lambda$, $\mu$, $\nu$ and $\rho$ be dominant weights of
$\mathfrak{sl_n}$ satisfying $\lambda + \mu = \nu + \rho$. Let $V_{\lambda}$
denote the highest weight module corresponding to $\lambda$. Lam, Postnikov,
Pylyavskyy conjectured a sufficient condition for $V_{\lambda} \otimes V_{\mu}$
to be contained in $V_{\nu} \otimes V_{\rho}$ as $\mathfrak{sl_n}$-modules. In
this note we prove a weaker version of the conjecture. Namely we prove that
under the conjectured conditions every irreducible $\mathfrak{sl_n}$-module
which appears in the decomposition of $V_{\lambda} \otimes V_{\mu}$ does appear
in the decomposition of $V_{\nu} \otimes V_{\rho}$.
