Aritmethic lattices of $\text{SO}(1,n)$ and units of group rings

We establish that standard arithmetic subgroups of a special orthogonal group $\mathrm{S}\mathrm{O}(1,n)$ are conjugacy separable. As an application we deduce this property for unit groups of certain integer group rings. We also prove that finite quotients of group of units of any of these group rings determines the original group ring.