  We give a short proof of Scharlemann's Strong Haken Theorem for closed
$3$-manifolds (and manifolds with spherical boundary). As an application, we
also show that given a decomposing sphere $R$ for a $3$-manifold $M$ that
splits off an $S^2 \times S^1$ summand, any Heegaard splitting of $M$ restricts
to the standard Heegaard splitting on the summand.
