On embedding of finitely generated profinite semigroups into 2-generated profinite semigroups

Koryakov recently asked the following question: when a pseudovariety V does not satisfy any non-trivial identify, does these exist an embedding from any finitely generated V-free profinite semigroup into the 2-generated V-free profinite semigroup? During the conference "Semigroups, Automata and Languages" in Porto (June 1994 [2]), a positive answer to this question was conjectured. We give here a counterexample to this conjecture.