  We show that the equivariant small quantum $K$-group of a partial flag
manifold is a quotient of that of the full flag manifold as a based ring. This
yields a variant of the $K$-theoretic analogue of the parabolic version of
Peterson's theorem [Lam-Shimozono, Acta Math. {\bf 204} (2010)] that exhibits
different shape from the case of quantum cohomology. This note can be seen as
an addendum to [K, arXiv:1805.01718 and arXiv:1810.07106].
