The conjecture on Fujimoto-interpretable finite approximations to Tarski biconditionals

Let $A$ be a finitely axiomatized Vaught theory in signature $\Theta_0$, let $N:A\rhd{\sf R}$, and suppose $\top\rhd_A{\sf TB}^{-}_N$. Finite-approximation conjecture. There is a $\beta$ such that \top\rhd_A\beta\mathrel{\text{\textcolor{gray}{\blacktriangleright}}}_A{\sf TB}^{-}_N. More generally, if $A$ is a finitely axiomatized Vaught theory and $\top\rhd_A V$, then there is a $B$ such that \top\rhd_A B\mathrel{\text{\textcolor{gray}{\blacktriangleright}}}_A V. The paper presents this as a second conjecture concerning finite axiomatizations and Fujimoto interpretability.