Let $M$ be an oriented matroid on the ground set $E$, and let $L(M)$ be its ranked poset of covectors. By definition, $L(M)$ is a sub-poset of the poset $\{0, \pm 1\}^E$, ordered by putting $0 < \pm 1$, with the rank being the number of nonzero coordinates. However, I want to consider $L(M)$ as an abstract ranked poset, rather than as a subposet of $\{0, \pm 1\}^E$.

Question 1: Is the oriented matroid $M$ determined, up to isomorphism, by $L(M)$?

Question 2: Is there a nice characterization of which ranked posets arise in this way?