The result below appears in the following article: On globally generated vector bundles on projective space.
Lemma 3. Let $\mathcal{E}$ be a globally generated vector bundles on $\mathbb{P}^{n}$ and let $\mathcal{E}^{*}$ denotes its dual bundle. If $h^{0}(\mathcal{E}^{*}) = r$, then there exists a globally generated vector bundle $\mathcal{E}^{'}$ such that $\mathcal{E} \cong \mathcal{E}^{'} \oplus\mathcal{O}_{\mathbb{P}^{n}}^{\oplus r}$ and $h^{0}(\mathcal{E}^{'}) = 0$.
In the demonstration of this result, the author says that:
Since $\mathcal{E}$is globally generated we have a surjection $$H^{0}(\mathcal{E}) \otimes \mathcal{O}_{\mathbb{P}^{n}} \longrightarrow \mathcal{E} \longrightarrow 0.$$
Since $h^{0}(\mathcal{E}^{*}) = r$, we have a surjection $$\mathcal{E} \longrightarrow \mathcal{O}_{\mathbb{P}^{n}}^{r} \longrightarrow 0.$$
He claims that the composition $$H^{0}(\mathcal{E}) \otimes \mathcal{O}_{\mathbb{P}^{n}} \longrightarrow \mathcal{O}_{\mathbb{P}^{n}}^{r} \longrightarrow 0,$$ necessarily splits, whence $$\mathcal{E} \longrightarrow \mathcal{O}_{\mathbb{P}^{n}}^{r} \longrightarrow 0.$$ also splits. Why?
Thanks in advance.