Conjecture on conforming heredity data and Ringel duals

Let $A_R$ be a based quasi-hereditary algebra over $R$ with conforming heredity data, and let $A'_R$ be a Ringel dual of $A_R$. Let $T^A(n,d)_\mathbb{F}$ and $T^{A'}(n,d)_\mathbb{F}$ denote the corresponding generalized Schur algebras after passage to $\mathbb{F}$. The conforming heredity and Ringel-duality conjecture. The algebra $A'_R$ has conforming heredity data. Moreover, when $d\leq n$, $T^{A'}(n,d)_\mathbb{F}$ is a Ringel dual of $T^A(n,d)_\mathbb{F}$. The conjecture addresses whether the structural heredity data survive Ringel duality and whether the generalized Schur construction commutes with that duality.