Symmetric monoidality of duality for almost perfect modules over the sphere spectrum

Let $A$ be a coherent connective commutative algebra over the sphere spectrum $\mathbb{S}$, and let $\APerf_A$ denote the category of almost perfect $A$-modules. Consider the $A$-linear duality functor

$$(-)^\vee \coloneqq \IntHom_A(-,A)\colon \APerf_A^{\op}\longrightarrow \Mod_A.$$

Sphere-spectrum duality claim. The result established for coherent, eventually coconnective commutative dg algebras over $\C$ also holds over $\mathbb{S}$: the restricted duality functor $(-)^\vee$ is symmetric monoidal.

This is a proposed extension of the preceding proposition from the complex numbers to the sphere spectrum. The supplied text gives no further evidence about whether the claim has been proved.