  As conjectured by T. Przebinda, the transfer of characters in the Howe's
correspondence should be obtained via the Cauchy-Harish-Chandra integral. In
this paper, we prove that the conjecture holds for the dual pair $(G = U(p, q),
G' = U(r, s))$, $p+q = r+s$, starting with a discrete series representation
$\Pi$ of $\widetilde{U}(p, q)$.
