The Stacks project

Remark 111.36.8. If $U \to X$ is a quasi-compact immersion then any quasi-coherent sheaf on $U$ is the restriction of a quasi-coherent sheaf on $X$. If $X$ is a Noetherian scheme, and $U \subset X$ is open, then any coherent sheaf on $U$ is the restriction of a coherent sheaf on $X$. Of course the exercise above is easier, and shouldn't use these general facts.