  Let $G \subseteq \tilde{G}$ be two quasisplit connected reductive groups over
a local field of characteristic zero and $G_{der} = \tilde{G}_{der}$. 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 that of $\tilde{G}$.
Motivated by this, we hope to construct the L-packets of $\tilde{G}$ from that
of $G$. The primary example in our mind is when $G = Sp(2n)$, whose L-packets
have been determined by Arthur (2013), and $\tilde{G} = GSp(2n)$. 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 $\tilde{G}$ from that of $G$.
