  In this note, we study submanifold geometry of the Atiyah-Hitchin manifold,
the double cover of the $2$-monopole moduli space. When the manifold is
naturally identified as the total space of a line bundle over $S^2$, the zero
section is a distinguished minimal $2$-sphere of considerable interest. In
particular, there has been a conjecture by Micallef and Wolfson [Math. Ann. 295
(1993), Remark on p.262] about the uniqueness of this minimal $2$-sphere among
all closed minimal $2$-surfaces. We show that this minimal $2$-sphere satisfies
the "strong stability condition" proposed in our earlier work
[arXiv:1710.00433], and confirm the global uniqueness as a corollary.
