Galois Alperin weight conjecture for a finite group

Fix a prime $p$ and a finite group $G$. Let $\mathcal{H}$ be the Galois automorphism group associated with the $p$-modular system in the source. Let $\mathcal{W}(G)$ be the set of $p$-weights of $G$, with the action of $\mathcal{H}\times\operatorname{Aut}(G)$ induced by Galois automorphisms and group automorphisms. Galois Alperin weight conjecture for $G$. There exists an $\mathcal{H}\times\operatorname{Aut}(G)$-equivariant surjective map

$$f:\mathcal{W}(G)\longrightarrow\operatorname{IBr}(G)$$

such that $f$ maps only $G$-conjugate weights to a common Brauer character. This formulation is equivalent to requiring a well-defined equivariant bijection between $G$-orbits of weights and irreducible Brauer characters. The source presents it as a conjecture, and no general resolution is stated.