Li's directed $C_4$ conjecture for oriented bipartite graphs

Let $D$ be an oriented bipartite graph with bipartition $(A,B)$, and let $d^+(x)$ denote the out-degree of a vertex $x$. A directed $C_4$ is a directed cycle of length four in $D$. Li's conjecture. If

$$d^{+}(u)>|B|/3$$

for each $u\in A$ and

$$d^{+}(v)>|A|/3$$

for each $v\in B$, then $D$ has a directed $C_4$. H. Li proposed this conjecture and proved it for balanced oriented bipartite graphs; the general statement is not resolved by the supplied text.