  We compute the Schur index of Argyres-Douglas theories of type
$(A_{N-1},A_{M-1})$ with surface operators inserted, via the Higgsing
prescription proposed by D. Gaiotto, L. Rastelli and S. S. Razamat. These
surface operators are obtained by turning on position-dependent vacuum
expectation values of operators in a UV theory which can flow to the
Argyres-Douglas theories. We focus on two series of $(A_{N-1},A_{M-1})$
theories; one with ${\rm gcd}(N,M)=1$ and the other with $M=N(k-1)$ for an
integer $k\geq 2$. For these two series of Argyres-Douglas theories, our
results are identical to the characters of non-vacuum modules of the associated
2d chiral algebras, which explicitly confirms a remarkable correspondence
recently discovered by C. Cordova, D. Gaiotto and S.-H. Shao.
