  Recently, Kuniba, Okado and Yamada proved that the transition matrix of
PBW-type bases of the positive-half of a quantized universal enveloping algebra
$U_q(\mathfrak{g})$ coincides with a matrix coefficients of the intertwiner
between certain irreducible modules over the corresponding quantized coordinate
ring $A_q(\mathfrak{g})$, introduced by Soibelman. In the present article, we
give a new proof of their result, by using representation theory of the
$q$-boson algebra, and the Drinfeld paring of $U_q(\mathfrak{g})$.
