  We give a short proof that every contracting self-similar group embeds into a
finitely presented simple group. In particular, any contracting self-similar
group embeds into the corresponding R\"over--Nekrashevych group, and this in
turn embeds into one of the twisted Brin--Thompson groups introduced by the
first author and Matthew Zaremsky. The proof here is a simplification of a more
general argument given by the authors, Collin Bleak, and Matthew Zaremsky for
contracting rational similarity groups.
