  We study a one-dimensional random walk among random conductances, with
unbounded jumps. Assuming the ergodicity of the collection of conductances and
a few other technical conditions (uniform ellipticity and polynomial bounds on
the tails of the jumps) we prove a quenched conditional invariance principle
for the random walk, under the condition that it remains positive until time
$n$. As a corollary of this result, we study the effect of conditioning the
random walk to exceed level $n$ before returning to 0 as $n\to \infty$.
