  We extend the results of arXiv:1401.1645 on the generalized conformal
Sp(2n)-structure of infinite multiplets of higher spin fields, formulated in
spaces with extra tensorial directions (hyperspaces), to the description of
OSp(1|2n)-invariant infinite-dimensional higher-spin supermultiplets formulated
in terms of scalar superfields on flat hyper-superspaces and on OSp(1|n)
supergroup manifolds. We find generalized superconformal transformations
relating the superfields and their equations of motion in flat hyper-superspace
with those on the OSp(1|n) supermanifold. We then use these transformations to
relate the two-, three- and four-point correlation functions of the scalar
superfields on flat hyperspace, derived by requiring the OSp(1|2n) invariance
of the correlators, to correlation functions on the OSp(1|n) group manifold. As
a byproduct, for the simplest particular case of a conventional N=1, D=3
superconformal theory of scalar superfields, we also derive correlation
functions of component fields of the scalar supermultiplet including those of
auxiliary fields.
