Unconditional Grün's lemma for conformal algebras

Determine whether conformal algebras satisfy an unconditional Grün's lemma; if they do not, provide a refined characterization of when the second-center coincides with the center for perfect conformal algebras.

Background

The paper explains that conformal algebras correspond to two-sorted conformal algebras and that these are equivalent to a Mal'cev variety of equational conformal algebras. Since the latter are expansions of an abelian group operation, they form a class of semiassociative Mal'cev algebras to which the paper's conditional Grün's lemma applies. The unresolved question is whether conformal algebras have the stronger unconditional property and, if not, how to characterize equality of their second-center and center in the perfect case.