  Let $K$ be an infinite field of characteristic $p>0$ and let $\lambda, \mu$
be partitions of $n$, where $\lambda=(\lambda_1,...,\lambda_n)$ and
$\mu=(\mu_1,..,\mu_n)$. By $S^{\lambda}$ we denote the Specht module
corresponding to $\lambda$ for the group algebra $K\mathfrak{S}_n$ of the
symmetric group $\mathfrak{S}_n$. D. Hemmer has raised the question of relating
the homomorphism spaces $\Hom_{\mathfrak{S}_n}(S^{\mu}, S^{\lambda})$ and
$\Hom_{\mathfrak{S}_{n'}}(S^{\mu^+}, S^{\lambda^+})$, where $n'=n+kp^d$,
$\lambda^+ =\lambda+(kp^{d})$, $\mu^+=\mu+(kp^{d})$, and $d, k$ are positive
integers. We show that these are isomorphic if $p$ is odd, $p^d
>\min\{\lambda_2, \mu_1-\lambda_1\}$ and $\mu_2 \le \lambda_1$.
