  Embeddings of the Racah algebra into the Bannai-Ito algebra are proposed in
two realizations. First, quadratic combinations of the Bannai-Ito algebra
generators in their standard realization on the space of polynomials are seen
to generate a central extension of the Racah algebra. The result is also seen
to hold independently of the realization. Second, the relationship between the
realizations of the Bannai-Ito and Racah algebras by the intermediate Casimir
operators of the $\mathfrak{osp}(1|2)$ and $\mathfrak{su}(1,1)$ Racah problems
is established. Equivalently, this gives an embedding of the invariance algebra
of the generic superintegrable system on the two-sphere into the invariance
algebra of its extension with reflections, which are respectively isomorphic to
the Racah and Bannai-Ito algebras.
