A note on hook length equidistribution on arithmetic progressions

In a recent paper, Bringmann, Craig, Ono, and the author showed that the number of $t$-hooks ($t\ge 2$) among all partitions of $n$ is not always asymptotically equidistributed on congruence classes $a(\mathrm{m}\mathrm{o}\mathrm{d}b)$. In this short note, we clarify the situation of $t=1$, i.e. all hook lengths, and show that this case does give asymptotic equidistribution, closing the story of the distribution properties of $t$-hooks on congruence classes.