Quantization conjecture for Poisson dynamical algebras

Let $L$ be an $ffrak{h}$-base manifold, let $P$ be an $ffrak{h}$-manifold, and let $pi$ be a Poisson dynamical bracket on $P$ over $L$. A quantization of the Poisson dynamical $ffrak{h}$-algebra $\mathcal{A}(P)$ is a pair $(\mathcal{L}_t,\mathcal{A}_t(P))$ in which $\mathcal{L}_t$ quantizes the Poisson base algebra $\mathcal{A}(L)$ and $\mathcal{A}_t(P)$ is a flat $\mathbb{C}[[t]]$-module and a dynamical associative $\mathcal{U}_t(\mathfrak{h})$-algebra over $\mathcal{L}_t$, with $\mathcal{A}_t(P)/t\mathcal{A}_t(P)=\mathcal{A}(P)$ and $a\mathbin{\divideontimes}b-b\mathbin{\divideontimes}a=t\pi(a,b)+O(t^2)$. Quantization conjecture. Any Poisson dynamical algebra can be quantized. This is an existence claim for deformation quantizations compatible with the dynamical base-algebra structure; the supplied text gives no evidence resolving it.