Let $A$ be a Hopf algebra over a field $k$. Let $B$ be a normal subHopf algebra of $A$. Is $A$ coflat over $A//B$? An explanation would be greatly appreciated.

(A novice to Hopf algebras, I am attempting to follow the computation of the homotopy of some Thom spectra in Kochman's book. Given $F$, an $A//B$-free coresolution of $k$, Kochman states that $F \Box_{A//B} A$ is an $A$-free coresolution of $k \Box_{A//B} A \cong B$. I don't see why $-\Box_{A//B} A$ preserves exactness.)