  In recent papers we demonstrated that consistent and non-trivial
\emph{linear} transformations of matter supermultiplets generate half-integer
superspin supercurrents and the cubic interactions between matter and
half-integer superspin supermultiplets. In this work we show that consistent
and non-trivial \emph{antilinear} transformations of matter superfields lead to
the construction of integer superspin supercurrents and the cubic interactions
between mater and integer superspin supermultiplets. Applying Noether's method
to these transformations, we find new integer superspin supercurrents for the
case of a free massless chiral superfield. Furthermore, we use them to find new
integer superspin supercurrent multiplets for a massive chiral superfield and a
chiral superfield with a linear superpotential. Also various selection rules
for such interactions are found.
