  We establish automorphisms with closed formulas on quasi-split
$\imath$quantum groups of symmetric Kac-Moody type associated to restricted
Weyl groups. The proofs are carried out in the framework of $\imath$Hall
algebras and reflection functors, thanks to the $\imath$Hall algebra
realization of $\imath$quantum groups in our previous work. Several quantum
binomial identities arising along the way are established.
