  Let $\mathfrak{g}=\mathfrak{sl}(\infty)$. We compute the annihilators of a
class of simple integrable weight $\mathfrak{g}$-modules with
finite-dimensional weight spaces. It is a claim of I. Dimitrov, that this class
exhausts all simple integrable weight $\mathfrak{g}$-modules with
finite-dimensional weight spaces. The main feature of interest is that
Dimitrov's class of modules contains non highest weight modules. Here we
provide another construction for these modules, which allows to apply results
of [PP18] to compute such annihilators.
