Infinitesimal-character conjecture for quasi-split groups over finite extensions

Let $F$ be a finite extension of ${\mathbb Q}_p$, and let $G$ be a quasi-split group over $F$. Infinitesimal-character conjecture for quasi-split groups. Does the infinitesimal-character conjecture for locally analytic vectors hold for $G(F)$? The question arises because the stated conjecture fails for the quaternion algebra $D$ due to its anisotropicness modulo its center; its validity for quasi-split groups over finite extensions remains open in the supplied text.