On the time of reaching a fixed level by a critical branching process in a random environment

Let $\{\xi_n\}$ be a critical branching process in a random environment with linear-fractional generating functions; let $T$ be the extinction time of $\{\xi_n\}$, and $T_x$ be the time of first passage of the semiaxis $(x,\infty)$. We find the asymptotic distributions of the random variables $T_x/\ln^2 x$, $T_x/T$, $T/\ln^2x$ under the condition $\{T_x<\infty\}$ as $x\to \infty$.