Specialization conjecture for the nonlocal integrals of motion

Let ${\cal G}_n(s)$ be the nonlocal integrals of motion for the deformed Virasoro algebra at parameter $s$, and let ${\cal G}_n^{DV}$ be the specialized nonlocal integrals defined at $s=2$. Nonlocal specialization conjecture. When $s$ tends to $2$,

$${\cal G}_n(s)\to {\cal G}_n^{DV},\qquad (s\to2).$$

The conjecture asserts that the general nonlocal construction specializes to the stated deformed Virasoro nonlocal integrals. The preceding formulas show simplifications at $s=2$, but the supplied text gives no resolution status.