  We consider the map of three-dimensional N=4 superfields to N=3 harmonic
superspace. The left and right representations of the N=4 superconformal group
are constructed on N=3 analytic superfields. These representations are
convenient for the description of N=4 superconformal couplings of the Abelian
gauge superfields with hypermultiplets. We analyze the N=4 invariance in the
non-Abelian N=3 Yang-Mills theory.
