Kaneko's finite multiple zeta algebra isomorphism conjecture

Let $\mathcal{Z}_{\mathscr{A}}^f$ be the formal finite multiple zeta space, and denote the formal symbol associated with $(k_1,\ldots,k_r)$ by $\zeta_{\mathscr{A}}^f(k_1,\ldots,k_r)$. Define

$$\zeta_{\mathcal{S}}^f(k_1,\ldots,k_r):=\sum_{j=0}^r(-1)^{k_{j+1}+\cdots+k_r}\zeta^f(k_1,\ldots,k_j)\zeta^f(k_r,\ldots,k_{j+1}).$$

Kaneko's conjecture. The map

$$\mathcal{Z}_{\mathscr{A}}^f\longrightarrow \mathcal{Z}^f/\zeta^f(2)\mathcal{Z}^f,\qquad \zeta_{\mathscr{A}}^f(k_1,\ldots,k_r)\longmapsto \zeta_{\mathcal{S}}^f(k_1,\ldots,k_r)$$

is an isomorphism of $\mathbb{Q}$-algebras. This relates formal finite multiple zeta values to the symmetric formal multiple zeta quotient; the source gives no resolution.