Moretó–Rizo character correspondence conjecture for subnormalisers

Let $G$ be a finite group and $p$ a prime. For a subgroup $H$ of $G$, define its subnormaliser by

$$\operatorname{Sub}_G(H)=\left\langle\{g\in G\mid H\triangleleft\triangleleft\langle g,H\rangle\}\right\rangle.$$

For an element $x\in G$, write $\operatorname{Sub}_G(x)=\operatorname{Sub}_G(\langle x\rangle)$, and let $\operatorname{Irr}^x(G)$ be the set of complex irreducible characters of $G$ that do not vanish at $x$.

Moretó–Rizo's character correspondence conjecture. For any $p$-element $x\in G$, there exists a bijection

$$f_x:\operatorname{Irr}^x(G)\to\operatorname{Irr}^x(\operatorname{Sub}_G(x))$$

such that, for every $\chi\in\operatorname{Irr}^x(G)$,

$$\chi(1)_p=f_x(\chi)(1)_p$$

and

$$\mathbb{Q}(\chi(x))=\mathbb{Q}(f_x(\chi)(x)).$$

This conjecture proposes a character correspondence between a finite group and the subnormaliser of a $p$-element, preserving the $p$-parts of character degrees and the fields generated by the corresponding character values. The source presents it as a recent conjecture motivating the study, but provides no resolution status.