Li and Yang's conjecture on sharing small functions with a derivative

Let $f$ be a non-constant entire function, let $k$ be an integer, and let $a_1$ and $a_2$ be two distinct small functions of $f$. Li and Yang's conjecture. If $f$ and $f^{(k)}$ share $a_1$ and $a_2$ IM, then $f\equiv f^{(k)}$. Theorem F establishes this conclusion for two distinct complex constants; the conjecture asks whether it remains true for arbitrary distinct small functions of $f$.