  This short paper is a continuation of the author's Ph.D thesis, where
Ekedahl-Oort strata are defined and studied for Shimura varieties of Hodge
type. The main results here are as follows.
  1. The Ekedahl-Oort stratification is independent of the choices of
symplectic embeddings.
  2. Under certain reasonable assumptions, there is certain functoriality for
Ekedahl-Oort stratifications with respect to morphisms of Shimura varieties.
