Suppose that $\mathcal{M}_1$ and $\mathcal M_2$ are two oriented matroids on the same ground set $E$. Under what conditions on $\mathcal{M}_1$ and $\mathcal{M}_2$ is there an oriented matroid $\mathcal{M}$ on the ground set $E\cup \{e\}$ such that $\mathcal{M}-e=\mathcal{M}_1$ and $\mathcal{M}/e=\mathcal{M}_2$?

I feel like I've seen the answer to this in the book, and that the necessary and sufficient condition was $\mathcal{T}(\mathcal{M}_2)\subset \mathcal{T}(\mathcal{M}_1),$ where $\mathcal{T}(\mathcal{M})$ is the set of topes of $\mathcal{M}$. However, I've been trying to find it in the book again without any success for a very long time.