The fundamental lemma for matching orbital integrals

Let $G$ be a reductive group over the local field $F$, let $H$ be an endoscopic group, and let $\gamma\in H(F)$ be strongly $G$-regular semisimple. Write $\Lambda_{G,H}(\gamma)$ for the corresponding linear combination of orbital integrals on $G$, and $\Lambda^{st}_H(\gamma)$ for the stable orbital integral on $H$. The fundamental lemma. For every $\gamma\in H(F)$ that is strongly $G$-regular semisimple,

$$\Lambda_{G,H}(\gamma)=\Lambda^{st}_H(\gamma).$$

This is the fundamental comparison predicted by the Langlands–Shelstad theory of endoscopy; the supplied text does not state whether it is known or remains open in the generality asserted.