Let $G$ be a connected,reductive group over a $p$-adic field $k$. Let $M_0$ be a minimal Levi subgroup of $G$, and define $M_0^{\operatorname{der}}$ to be $M_0 \cap G_{\operatorname{der}}$. Lemma 2.1 of this paper by Takuya Konno on the Langlands classification for $p$-adic groups comes down to showing that

$$H^1(k, M_0^{\operatorname{der}}) \rightarrow H^1(k, G_{\operatorname{der}})$$

is injective. He claims that this is equivalent to Proposition 4.7 and Theorem 4.13 of the article *Groupes Reductifs* by Borel and Tits. These results are about conjugacy of minimal parabolics and Levis for a reductive group $G$ over an arbitrary field $k$:

Propostion 4.7: Let $P,P'$ be two parabolic $k$-subgroups of $G$. Then $P \cap P'$ contains a maximal torus defined over $k$. Every connected $k$-closed subgroup of $P \cap P'$ is defined over $k$. In particular, $P \cap P', \mathscr R(P \cap P'), \mathscr R_u(P \cap P')$ are defined over $k$. The group $P \cap P'$ has Levi $k$-subgroups, and any two of them are conjugate by a unique element of $\mathscr R_u(P \cap P')(k)$.

Theorem 4.13: Let $P, P'$ be two parabolic $k$-subgroups of $G$.a) The fibration of $G$ by $P$ has a local section defined over $k$; the projection $G(k) \rightarrow G/P(k)$ is surjective.

b) If $P$ and $P'$ are minimal (among parabolic $k$-subgroups), they are conjugate over $k$.

c) If $P$ and $P'$ are conjugate over an extension of $k$, then they are conjugate over $k$.

I don't understand the connection between these results and the claim in the lemma. How can one interpret these results about the conjugacy of minimal parabolics as as a statement of injectivity of the $H^1$ sets?