Sun–Wang–Yao transformation conjecture for strongly graceful trees

Let $T$ be a tree with a perfect matching. An adding-edge-subtracting dual graph transformation replaces an edge $u_{k-1}v_{k-1}\in E(H_{k-1})$ by an edge $x_ky_k\notin E(H_{k-1})$ according to

$$H_k=H_{k-1}+x_ky_k-u_{k-1}v_{k-1},$$

for $k\in[1,m]$, with $H_0=T$ and $H_m=P$. Sun–Wang–Yao conjecture. Any such tree $T$ with a perfect matching can be transformed into a certain path $P$ with a perfect matching through these transformations, such that both $T$ and $P$ admit strongly graceful labelings. The claim concerns preservation of strong graceful labelability along a transformation sequence; the source gives no resolution.