  We determine the asymptotic quantum variance of microlocal lifts of
Hecke--Maass cusp forms on the arithmetic compact hyperbolic surfaces attached
to maximal orders in quaternion algebras. Our result extends those of
Luo--Sarnak--Zhao concerning the non-compact modular surface. The results of
this article's prequel (which involved the theta correspondence, Rallis inner
product formula and equidistribution of translates of elementary theta
functions) reduce the present task to some local problems over the reals
involving the construction and analysis of microlocal lifts via integral
operators on the group. We address these here using an analytic incarnation of
the method of coadjoint orbits.
