Finitely generated infinite torsion groups that are residually finite simple

We show that every finitely generated residually finite torsion group $G$ embeds in a finitely generated torsion group $\mathrm{\Gamma }$ that is residually finite simple. In particular we show the existence of finitely generated infinite torsion groups that are residually finite simple, which answers a question of Olshanskii and Osin.