  We prove that the global geometric theta-lifting functor for the pair (H, G)
is compatible with the Whittaker normalization, where (H,G) is one of the pairs
(SO_{2n}, Sp_{2n}), (Sp_{2n}, SO_{2n+2}) or (GL_{n},GL_{n+1}). That is, the
composition of the theta-lifting functor from H to G with the Whittaker functor
for G is isomorphic to the Whittaker functor for H.
