The generation conjecture for invariants of current Lie superalgebras

Let $\mathfrak{g}$ be the Lie superalgebra considered in the paper, let $B$ be an associative, commutative, finitely generated algebra with unity, and let $U(\mathfrak{g}\otimes B)^{\mathfrak{g}}$ denote the subalgebra of $\mathfrak{g}$-invariants in the universal enveloping algebra $U(\mathfrak{g}\otimes B)$. For $a_1,\ldots,a_k\in B$, let $T_k(a_1,\ldots,a_k)$ be the image in $U(\mathfrak{g}\otimes B)$ of the corresponding tensor $\widetilde{T}_k(a_1,\ldots,a_k)$, and let $T(B)$ be the algebra generated by these elements.

Generation conjecture. Let $T(B)$ be the algebra generated by $T^k(a_1,\ldots,a_k)$ where $a_1,a_2,\ldots,a_k\in B$ and $k\in\mathbb{Z}_{+}$. Then

$$T(B)=U(\mathfrak{g}\otimes B)^{\mathfrak{g}}.$$

This asserts that the explicitly constructed generalized Casimir elements generate all elements invariant under the adjoint action of $\mathfrak{g}$ in the enveloping algebra of the current Lie superalgebra. The supplied text gives no resolution status, so the claim remains open here.