  We consider a L\'evy process that starts from $x<0$ and conditioned on having
a positive maximum. When Cram\'er's condition holds, we provide two weak limit
theorems as $x\to -\infty$ for the law of the (two-sided) path shifted at the
first instant when it enters $(0,\infty)$, respectively shifted at the instant
when its overall maximum is reached. The comparison of these two asymptotic
results yields some interesting identities related to time-reversal, insurance
risk, and self-similar Markov processes.
