Freyd's Generating Hypothesis for the p-completed Spanier–Whitehead category

Let ${\mathcal{F}}_p$ be the $p$-completed Spanier–Whitehead category, contained as the full subcategory of strongly dualisable objects in a semi-Freyd category ${\mathcal{M}}_p$. Let $R$ be the stable homotopy ring associated with ${\mathcal{M}}_p$, and consider

$$\pi_*:{\mathcal{F}}_p\to\operatorname{Mod}_R.$$

Freyd's Generating Hypothesis for ${\mathcal{F}}_p$. The functor $\pi_*$ is faithful. Therefore, ${\mathcal{M}}_p$ is a Freyd category, with ${\mathcal{F}}_p$ as its full subcategory of strongly dualisable objects. The source states that this formulation is equivalent to the original Freyd Generating Hypothesis, but gives no evidence of resolution.