Strongly supercritical branching process in a random environment dying at a distant moment

Let $\left\{ Z_{i},\text{ }i=0,1,\ldots \right\} $ be a strongly supercritical branching process in a random environment. It is assumed that the reproduction laws of particles in different generations are geometric. Let $T$ be the extinction time of the specified process. It is shown that the coordinates of a random vector $\left( Z_{0},Z_{1},\ldots ,Z_{n}\right)$ with numbers distant from each other and from $0$ and $n$ are asymptotically independent, provided that $n<T<+\infty $, $n\rightarrow \infty $, and have the same limiting distribution.