Is every sheaf a subsheaf of a flasque sheaf?

Question

Call a sheaf flasque if for all open sets $U \subset V$, the restriction map$$\mathcal{F}(V) \to \mathcal{F}(U)$$is surjective. Is every sheaf a subsheaf of a flasque sheaf?

Answer 1

Let$$\mathcal{G} = \prod_{p \in X} \mathcal{F}_p.$$Then $\mathcal{F}$ is a subsheaf of $\mathcal{G}$ and $\mathcal{G}$ is easily seen to be flasque.