  We write explicitly a transformation of the scattering phases reducing the
problem of quantum chaotic scattering for systems with M statistically
equivalent channels at nonideal coupling to that for ideal coupling. Unfolding
the phases by their local density leads to universality of their local
fluctuations for large M. A relation between the partial time delays and
diagonal matrix elements of the Wigner-Smith matrix is revealed for ideal
coupling. This helped us in deriving the joint probability distribution of
partial time delays and the distribution of the Wigner time delay.
