Let $m\ge 2$, and let $\nu=(\nu_1,\dots,\nu_m)$ be a weakly decreasing sequence of nonnegative integers, viewed as a partition with at most $m$ parts and with trailing zero parts allowed. Let $B_m(\nu)$ denote the type $A_{m-1}$ highest weight crystal for $\mathfrak{gl}_m$ realized as the set of semistandard Young tableaux of shape $\nu$ with entries in $\{1,\dots,m\}$, whose rows are weakly increasing from left to right and whose columns are strictly increasing from top to bottom, with Kashiwara operators $e_i,f_i:B_m(\nu)\to B_m(\nu)\sqcup\{0\}$ for $1\le i\le m-1$ defined by the type $A$ reading-word signature rule. Restrict $B_m(\nu)$ to a type $A_{m-2}$, equivalently $\mathfrak{gl}_{m-1}$, crystal by retaining only the operators $e_i,f_i$ with $1\le i\le m-2$ and keeping the same underlying set. Then there is an isomorphism of $\mathfrak{gl}_{m-1}$-crystals $\operatorname{Res}^{\mathfrak{gl}_m}_{\mathfrak{gl}_{m-1}} B_m(\nu) \cong \bigsqcup_{\mu} B_{m-1}(\mu)$, where, for each summand, $B_{m-1}(\mu)$ is the semistandard tableau crystal of shape $\mu$ with entries in $\{1,\dots,m-1\}$ and operators $e_i,f_i:B_{m-1}(\mu)\to B_{m-1}(\mu)\sqcup\{0\}$ for $1\le i\le m-2$, and where the disjoint union ranges over all weakly decreasing sequences of nonnegative integers $\mu=(\mu_1,\dots,\mu_{m-1})$ satisfying $\nu_i \ge \mu_i \ge \nu_{i+1}$ for every $1\le i\le m-1$. Equivalently, after setting $\mu_m:=0$, the skew diagram $\nu/\mu$ is a horizontal strip.