  In this paper, we investigate the structure of the convergent quantization of
the 1-shifted cotangent bundle $S$ of a smooth scheme $X$ over a perfect field
of positive characteristic. The quantization is an $E_2$-algebra over the
Frobenius twist $S'$ of the 1-shifted cotangent bundle which restricted to the
zero section $X'\rightarrow S'$ is weakly $E_2$-Morita equivalent to the
structure sheaf $\mathscr O_{X'}$ of the Frobenius twist $X'$ of $X$.
  Explicitly, we show that the $(\infty,2)$-category of coherent (left-)modules
over $\mathscr O_{X'}$ is equivalent to the full subcategory of the
$(\infty,2)$-category of coherent (left-)modules over the quantization
restricted to the zero section generated by $\mathscr O_X$ are equivalent.
