In this article we solve the isomorphism problem for subgroups of integral points of two-spherical Kac-Moody groups over the rational numbers.Along the way we establish versions of Mostow-Margulis strong rigidity and Margulis superrigidity with target in two-spherical split Kac-Moody groups over the rational numbers for arithmetically defined subgroups.
Parsa et al. (Fri,) studied this question.