The universal ring and pro-Hall embedding conjecture for fully residually free pro-p groups

Let $\mathbb{F}$ be a free pro-$p$ group. Let the universal class of $\mathbb{Z}_p$ consist of the relevant $\mathbb{Z}_p$-rings in the language with constants, and let a fully residually free pro-$p$ group be a pro-$p$ group discriminated by $\mathbb{F}$. For a finitely generated such group $G$, let $R(G)$ denote a finitely generated binomial $\mathbb{Z}_p$-algebra. The universal ring conjecture. (1) Every finitely generated fully residually $\mathbb{F}$ pro-$p$ group $G$ admits a finitely generated binomial $\mathbb{Z}_p$-algebra $R(G)$ from the universal class such that $G$ embeds into $\mathbb{F}(A,R(G))$. (2) The universal class contains a $\mathbb{Z}_p$-ring $S$ such that every finitely generated fully residually $\mathbb{F}$ pro-$p$ group embeds into $\mathbb{F}(A,S)$, where $S$ is fully residually $\mathbb{Z}_p$ and every finitely generated $\mathbb{Z}_p$-ring in the universal class is a subring of $S$. The source states this converse as a conjecture and gives no resolution.