SO$(2,n)$-compatible embeddings of conformally flat $n$-dimensional submanifolds in ${\mathbb{R}}^{n+2}$

We describe embeddings of $n$-dimensional Lorentzian manifolds, including Friedmann-Lemaître-Robertson-Walker spaces, in ${\mathbb{R}}^{n+2}$ such that the metrics of the submanifolds are inherited by a restriction from that of ${\mathbb{R}}^{n+2}$, and the action of the linear group SO$(2,n)$ of the ambient space reduces to conformal transformations on the submanifolds.