The $q$-Onsager algebra $O_q$ is presented by two generators $W_0$, $W_1$ and relations, called the $q$-Dolan/Grady relations. Recently Baseilhac Koizumi introduced a current $\mathcal A_q$ for $O_q$. Soon afterwards, Shigechi gave presentation of We show that these give PBW basis A_q$. Using this basis, we isomorphic to $O_q \otimes \mathbb F \lbrack z_1, z_2, \ldots \rbrack$, where $\mathbb F...