On unattainability of infinity boundary of domain for a diffusion semi-Markov process with stop

One-dimensional continuous semi-Markov process of diffusion type is considered on an interval with one infinite boundary. Semi-Markov transition generating functions of the process satisfy ordinary differential equation of the second order. Coefficients of this equation determine distribution of beginning of infinite stop of the process. In terms of these coefficients one sufficient condition proved for the right boundary to be unattainable.