Let $G$ be an algebraic group. We can try to reconstruct $G$ from its lie algebra $\mathfrak{g}$, but the best we get in general is a formal group scheme $\operatorname{Spf}(U(\mathfrak{g})^*)$, where $U(\mathfrak{g})$ is the universal enveloping algebra of $\mathfrak{g}$.

However, I have heard that certain conditions provide for a full reconstruction of $G$. Namely, if $G$ is connected and simply connected, then there is an isomorphism $\mathcal{O}(G) \rightarrow U(\mathfrak{g})^{\circ}$, where $U(\mathfrak{g})^{\circ}$ is the Hopf dual of $U(\mathfrak{g})$.

I can't seem to find a reference for this. Could someone please provide one?