  We develop an approach to Malliavin calculus for L\'evy processes from the
perspective of expressing a random variable $Y$ by a functional $F$ mapping
from the Skorohod space of c\`adl\`ag functions to $\mathbb{R}$, such that
$Y=F(X)$ where $X$ denotes the L\'evy process. We also present a
chain-rule-type application for random variables of the form
$f(\omega,Y(\omega))$.
  An important tool for these results is a technique which allows us to
transfer identities proved on the canonical probability space (in the sense of
Sol\'e et al.) associated to a L\'evy process with triplet
$(\gamma,\sigma,\nu)$ to an arbitrary probability space
$(\Omega,\mathcal{F},\mathbb{P})$ which carries a L\'evy process with the same
triplet.
