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Several ongoing surveys, notably by TESS and Gaia missions, are likely to discover star-black hole binaries in our Galaxy in the near future. A fraction of them may be triple systems comprising an inner binary, instead of a single black hole. They may be progenitors of the BBHs discovered from the gravitational wave. If such a star-binary black-hole system exists in our Galaxy, its outer tertiary star should exhibit a radial velocity modulation reflecting the nature of the inner binary. Combining an analytic approximation based the quadruple perturbation theory and N-body simulations of such triples, we examined the detectability of wide-separation inner BBHs in the Galaxy from the characteristic signals of the radial velocity of the tertiary star. The resulting radial velocities consist of two different types of modulations, short-term radial-velocity variations of roughly twice the orbital frequency of the inner BBH, and long-term modulations in significantly inclined triples. The latter is due to the precession of the inner and outer orbits over roughly the von Zeipel-Kozai-Lidov oscillation timescale. We conclude that it is quite feasible to detect such radial velocity modulations if those triples exist in our Galaxy.