Let $G$ be a finite group, $H$ a subgroup of $G$. The centralizer algebra of $H$ is the subalgebra of the group algebra $kG$ over a field $k$ that consists of elements commuting with $H$. As part of a larger project, Ellers and Murray have been working to uncover information about the blocks and the simple modules of these centralizer algebras. In this talk, we will address the problem of classifying the simple modules of centralizer algebras of symmetric groups $S_l$ in $S_n$. We will examine a potential solution to the problem proposed by Ellers and Murray, which was inspired by a classification of James for the simple $kS_n$-modules.