  We apply the general theory of codimension one integrability conditions for
$G$-structures developed in arXiv:1306.6817v3 [math.DG] to the case of
quaternionic CR geometry. We obtain necessary and sufficient conditions for an
almost CR quaternionic manifold to admit local immersions as an hypersurface of
the quaternionic projective space. We construct a deformation of the standard
quaternionic contact structure on the quaternionic Heisenberg group which does
not admit local immersions in any quaternionic manifold.
