A concatenated Friedkin-Johnsen (FJ) model is a two time-scale opinion dynamics model in which stubborn agents discuss a sequence of issues. For each issue, a FJ model is adopted, and concatenation refers to the fact that the final opinion of the agents at issue s becomes the initial condition at issue s + 1. In this paper we deal with the case in which the system is open, i.e., the group of interacting agents changes at each issue, and so does their stubbornness. A concatenated FJ model can in this case be represented as an infinite product of stochastic matrices. For such system, we obtain sufficient conditions under which the opinions of the agents converge to consensus.