  Let $G\subset\hat{G}$ be two complex connected reductive groups. We deals
with the hard problem of finding sub-$G$-modules of a given irreducible
$\hat{G}$-module. In the case where $G$ is diagonally embedded in
$\hat{G}=G\times G$, S. Kumar and O. Mathieu found some of them, proving the
PRV conjecture. Recently, the authors generalized the PRV conjecture on the one
hand to the case where $\hat{G}/G$ is spherical of minimal rank, and on the
other hand giving more sub-$G$-modules in the classical case $G\subset G\times
G$. In this paper, these two recent generalizations are combined in a same more
general result.
