Hartl's finitely generated value-group conjecture for weakly admissible points

Let $\breve E$ be the local Shimura field and let $\breve{\cal{F}}^0_b\subset\breve{\cal{F}}^{wa}_b$ be the intrinsic open locus defined from the associated filtered isocrystals. Let $L/\breve E$ be a complete valued extension whose value group is finitely generated.

Hartl's value-group conjecture. One has

$$\breve{\cal{F}}^0_b(L)=\breve{\cal{F}}^{wa}_b(L).$$

This would extend the equality already known in the paper for finite extensions of $\breve E$ and is used as evidence for the connectedness of $\breve{\cal{F}}^0_b$. Its general validity is left open.