  let $\widetilde{\bf U}^\imath$ be a quasi-split universal $\imath$quantum
group associated to a quantum symmetric pair $(\widetilde{\bf U},
\widetilde{\bf U}^\imath)$ of Kac-Moody type with a diagram involution $\tau$.
We establish the Serre-Lusztig relations for $\widetilde{\bf U}^\imath$
associated to a simple root $i$ such that $i \neq \tau i$, complementary to the
Serre-Lusztig relations associated to $i=\tau i$ which we obtained earlier. A
conjecture on braid group symmetries on $\widetilde{\bf U}^\imath$ associated
to $i$ disjoint from $\tau i$ is formulated.
