How to prove that a sequence of Galton-Watson processes converges in distribution to another Galton-Watson process?

Question

Let $ X^n = \lbrace X^n(t) : t = 0,1,2,... \rbrace $ and $ X = \lbrace X(t) : t = 0,1,2,... \rbrace $ be Galton-Watson processes with offspring generating function $ f_n $ and $ f $, respectively, such that $ f_n $ converges to $ f $ at every point. Is it true that $ X^n $ converges in distribution to $ X $ ? Is there any condition for this to happen?