Let $L$ be a language and $\mathcal{M},\mathcal{N}$ be $L$-structures. Suppose $\mathcal{M}$ and $\mathcal{N}$ are elementarily equivalent. Prove that there is some $L$-structure $\mathcal{R}$ and elementary embeddings $f:\mathcal{M} \rightarrow \mathcal{R}$ and $g:\mathcal{N} \rightarrow \mathcal{R}$.
My first attempt was to take $\mathcal{R}=\mathcal{N}$. Then the identity map is an elementary embedding from $\mathcal{N}$ to $\mathcal{R}$. It remains to show there is an elementary embedding from $\mathcal{M}$ to $\mathcal{N}$. However, being elementarily equivalent does not imply the existence of elementary embedding. So my method wouldn't work.
Then I have to construct this $L$-structure $\mathcal{R}$ so to make it satisfy the desired property. How can I construct it?