Computation of an étale cohomology group on the projective line

Question

I have the following problem: Let $U_{0}$ be a a smooth geometrically irreducible affine curve over $\mathbb{F}_{q}$, and let $\mathcal{E}_{0}$ be a constructible étale sheaf of $\mathbb{Q}_{\ell}$-vector spaces on $U_{0}$. By $\mathbb{F}$ we denote an algebraic closure of $\mathbb{F}_{q}$ and by $\mathbb{P}^{1}$ we denote the projective space over $\mathbb{P}^{1}$. By $U$ we denote the base change of $U_{0}$ to $\mathbb{F}$ and by $\mathcal{E}$ we denote the inverse image of $\mathcal{E}_{0}$ on $U$. Further, we denote by $j$ the inclusion of $U$ into $\mathbb{P}^{1}$ and by $i$ we denote the inclusion of its complements to $\mathbb{P}^{1}$. Then $$H^{1}_{ét}(\mathbb{P}^{1}, i_{*}i^{*}j_{*}\mathcal{E})=0.$$ This is what i don't understand. I am interested in this, because i want to deduce from the cohomology sequence of $$ 0\rightarrow j_{!}j^{*}j_{*}\mathcal{E}\rightarrow j_{*}\mathcal{E}\rightarrow i_{*}i^{*}j_{*}\mathcal{E}\rightarrow 0$$ that $$H_{c}^{1}(U,\mathcal{E})\twoheadrightarrow H_{ét}^{1}(\mathbb{P}^{1}, j_{*}\mathcal{E}).$$ I hope somebody can help me with this problem! Many thanks in advance