An interesting aspect to study on the topic of semigroups are their closure properties. In particular, this work aims to expand on previous results on the closure under the semigroup free product. These results stem from work done by Tara Brough and Alan J. Cain, who proved that automaton semigroups which have an idempotent or are homogeneous will form an automaton semigroup under the free product. In this work, we show that these restrictions can be loosened to encompass a greater number of automaton semigroups. We accomplish this by proving that two automaton semigroups form another automaton semigroup under free product construction, if there exist maps between their state sets that each extend into homomorphisms between their generated semigroups.