The generalized prefix expansion of inverse semigroups, presented by Lawson,
Margolis and Steinberg, is suitably modified to define an expansion for weakly left ample semigroups. We consider the class of FA-morphisms between weakly
left ample semigroups and show that this expansion gives rise to a universal FA-morphism onto a weakly left ample semigroup. The methods used are necessarily
different from the ones applied in the inverse case. We show how the inverse case can be deduced from this more general situation.