  Let $F$ be a non-Archimedean local field of characteristic $0$, let $G$ be
the group of $F$-rational points of a connected reductive group defined over
$F$ and let $G'$ be the group of $F$-rational points of its quasi-split inner
form. Given standard modules $I(\tau ,\nu )$ and $I(\tau ',\nu ')$ for $G$ and
$G'$ respectively with $\tau '$ a generic tempered representation, such that
the Harish-Chandra's $\mu $-functions of a representation in the supercuspidal
support of $\tau $ and of a generic essentially square-integral representation
in some Jacquet module of $\tau '$ agree (after a suitable identification of
the underlying spaces under which $\nu =\nu '$), we show that $I(\tau ,\nu )$
is irreducible whenever $I(\tau ',\nu ')$ is.
  The conditions are satisfied if the Langlands quotients $J(\tau ,\nu )$ and
$J(\tau ',\nu ')$ of respectively $I(\tau ,\nu )$ and $I(\tau ',\nu ')$ lie in
the same Vogan $L$-packet (whenever this Vogan $L$-packet is defined), proving
that, for any Vogan $L$-packet, all the standard modules whose Langlands
quotient is equal to a member of the Vogan $L$-packet are irreducible, if and
only if this Vogan $L$-packet contains a generic representation.
  The result for generic Vogan $L$-packets of quasi-split orthogonal and
symplectic groups was proven by Moeglin-Waldspurger and used in their proof of
the general case of the local Gan-Gross-Prasad conjectures for these Groups.
