Identities for a parametric Weyl algebra over a ring

In 2013 Benkart, Lopes and Ondrus introduced and studied in a series of papers the infinite-dimensional unital associative algebra ${\text{A}}_h$ generated by elements $x,y,$ which satisfy the relation $yx-xy=h$ for some $0\neq h\in \FF[x]$\mathrm{.}Wegeneralizethisconstructionto$\A_h(\B)$ by working over the fixed $\text{FF}$-algebra $\text{B}$ instead of $\text{FF}$. We describe the polynomial identities for ${\text{A}}_h(\text{B})$ over the infinite field $\text{FF}$ in case $h\in \text{B}[x]$ satisfies certain restrictions.