Conditioned stable random walk with a negative drift

Let $(S_n, n\ge 0)$ be a random walk with a negative drift, $T=\min\{n\colon S_n\le 0\}$. We prove that if the Cramer's type conditions are satisfied then there exists a constant $\Delta>0$ such that the random functions $S_{[nt]}/ \Delta n^{1/2}$, $0\le t\le 1$ considered under the condition $T>n$, converge weakly to a Brownian excursion when $n\to\infty$.