CM-liftability of simple superspecial abelian surfaces over prime fields

For any prime $p>0$, we prove that simple superspecial abelian surfaces over $\mathbb{F}_{p}$ admit CM liftings, by using the residual reflex condition (RRC) and Lie types. The CM-liftability of ordinary simple abelian surfaces is proved by Serre-Tate, and the CM-liftability of almost ordinary simpl