Hopf algebra isomorphism between the quantum toroidal algebra and the FRT algebra

Let $\mathcal{U}$ be the Hopf subalgebra obtained by the FRT formalism from the family of geometric $R$-matrices, and let

$$\Upsilon: U_{q_1,\frac{1}{q_2}}(\ddot{\mathfrak{gl}}_1)\Big|_{c=1,\,\psi_0^+=1,\,\psi_0^-=(q_1q_2)^{-r}}\longrightarrow \prod_{r=1}^{\infty}\operatorname{End}_{\mathbb{F}_r}\left(K^{T_r}(\mathcal{M}(r))_{\mathrm{loc}}\right)$$

be the algebra homomorphism described in the source.

Hopf algebra isomorphism conjecture. The map $\Upsilon$ induces a Hopf algebra isomorphism

$$U_{q_1,\frac{1}{q_2}}(\ddot{\mathfrak{gl}}_1)\Big|_{c=1,\,\psi_0^+=1,\,\psi_0^-=(q_1q_2)^{-r}}\xrightarrow{\sim}\mathcal{U}.$$

This conjecture would identify the specialized quantum toroidal algebra with the Hopf algebra reconstructed from the geometric $R$-matrices through the FRT formalism. The source gives no evidence of a proof or disproof.