The property $R_{\infty}$ conjecture for finitely presented $S$-arithmetic subgroups of Borel groups

Let $\mathbf{B}$ be a Borel subgroup of a split, connected, reductive, non-commutative linear algebraic group $\mathbf{G}$, all defined over a global field. An $S$-arithmetic subgroup is finitely presented if it admits a finite presentation, and a group has property $R_{\infty}$ if every automorphism has infinitely many twisted conjugacy classes. Property $R_{\infty}$ conjecture. All finitely presented $S$-arithmetic subgroups of $\mathbf{B}$ which are not virtually polycyclic have property $R_{\infty}$. This would extend the results for the soluble $S$-arithmetic groups considered in the paper to Borel subgroups of split reductive groups; the claim is presented as a conjectural consequence of the geometric and algebraic structure discussed above, and no resolution is supplied here.