  We characterise the integrability of any co-CR quaternionic structure in
terms of the curvature and a generalized torsion of the connection. Also, we
apply this result to obtain, for example, the following. (1) New co-CR
quaternionic structures built on vector bundles over a quaternionic manifold M,
whose twistor spaces are holomorphic vector bundles over the twistor space Z of
M. Moreover, all the holomorphic vector bundles over Z, which are positive and
isotypic when restricted to the twistor lines, are obtained this way. (2) Under
generic dimensional conditions, any manifold endowed with an almost
f-quaternionic structure and a compatible torsion free connection is, locally,
a product of a hypercomplex manifold with some power of the space of imaginary
quaternions.
