Equality of real Schur representation sets for finite-dimensional Jacobian algebras

Let $A$ be a finite-dimensional Jacobian algebra. Consider the three sets of real Schur representations: all real Schur representations; those constructed from the stated Schur-representation lemma; and those constructed from exchange pairs. The latter two sets are contained in the preceding ones. Equality conjecture. These three sets are equal for finite-dimensional Jacobian algebras. This asks whether every real Schur representation arises from the two specified constructions; the source gives no resolution status.