Let G be a graph. Denote by Li(G) its i-iterated line graph and denote by W(G) its Wiener index. Dobrynin, Entringer and Gutman stated the following problem: Does there exist a non-trivial tree T and i ≥ 3 such that W(Li(T)) = W(T)? In a series of five papers we solve this problem. In a previous paper we proved that W(Li(T)) > W(T) for every tree T that is not homeomorphic to a path, claw K1,3 and to the graph of "letter H", where i ≥ 3. Here we prove that W(Li(T)) > W(T) for every tree T homeomorphic to the claw, T ≠ K1,3 and i ≥ 4.