Let
$G$
be the
$F$
-rational points of the symplectic group
$S{{p}_{2n}}$
, where
$F$
is a non-Archimedean local field of characteristic 0. Cogdell, Kim, Piatetski-Shapiro, and Shahidi constructed local Langlands functorial lifting from irreducible generic representations of
$G$
to irreducible representations of
$G{{L}_{2n+1}}\left( F \right)$
. Jiang and Soudry constructed the descent map from irreducible supercuspidal representations of
$G{{L}_{2n+1}}\left( F \right)$
to those of
$G$
, showing that the local Langlands functorial lifting from the irreducible supercuspidal generic representations is surjective. In this paper, based on above results, using the same descent method of studying
$S{{O}_{2n+1}}$
as Jiang and Soudry, we will show the rest of local Langlands functorial lifting is also surjective, and for any local Langlands parameter
$\phi \,\in \,\Phi \left( G \right)$
, we construct a representation
$\sigma $
such that
$\phi $
and
$\sigma $
have the same twisted local factors. As one application, we prove the
$G$
-case of a conjecture of Gross-Prasad and Rallis, that is, a local Langlands parameter
$\phi \,\in \,\Phi \left( G \right)$
is generic, i.e., the representation attached to
$\phi $
is generic, if and only if the adjoint
$L$
-function of
$\phi $
is holomorphic at
$s\,=\,1$
. As another application, we prove for each Arthur parameter
$\psi $
, and the corresponding local Langlands parameter
${{\phi }_{\psi }}$
, the representation attached to
${{\phi }_{\psi }}$
is generic if and only if
${{\phi }_{\psi }}$
is tempered.