  We prove that every finitely presented self-similar group embeds in a
finitely presented simple group. This establishes that every group embedding in
a finitely presented self-similar group satisfies the Boone-Higman conjecture.
The simple groups in question are certain commutator subgroups of
R\"over-Nekrashevych groups, and the difficulty lies in the fact that even if a
R\"over-Nekrashevych group is finitely presented, its commutator subgroup might
not be. We also discuss a general example involving matrix groups over certain
rings, which in particular establishes that every finitely generated subgroup
of $\mathrm{GL}_n(\mathbb{Q})$ satisfies the Boone-Higman conjecture.
