Let
$G\subseteq \widetilde{G}$
be two quasisplit connected reductive groups over a local field of characteristic zero and having the same derived group. Although the existence of L-packets is still conjectural in general, it is believed that the L-packets of
$G$
should be the restriction of those of
$\widetilde{G}$
. Motivated by this, we hope to construct the L-packets of
$\widetilde{G}$
from those of
$G$
. The primary example in our mind is when
$G=\text{Sp}(2n)$
, whose L-packets have been determined by Arthur [The endoscopic classification of representations: orthogonal and symplectic groups, Colloquium Publications, vol. 61 (American Mathematical Society, Providence, RI, 2013)], and
$\widetilde{G}=\text{GSp}(2n)$
. As a first step, we need to consider some well-known conjectural properties of L-packets. In this paper, we show how they can be deduced from the conjectural endoscopy theory. As an application, we obtain some structural information about L-packets of
$\widetilde{G}$
from those of
$G$
.