Correlation of B(s) --> mu(+)mu(-) and (g - 2)(mu) in minimal supergravity.

We analyze the decay mode B(s)-->mu(+)mu(-) in minimal supergravity (mSUGRA). We find that the recently measured excess in (g-2)(mu), if interpreted within mSUGRA, is correlated with a substantial enhancement of the branching ratio Beta(B(s)-->mu(+)mu(-)): if (g-2)(mu) exceeds the standard model prediction by 4 x 10(-9), Beta(B(s)-->mu(+)mu(-)) is larger by a factor of 10-100 and within reach of Run-II of the Tevatron. Thus the search for B(s)-->mu(+)mu(-) is a stringent test of the GUT scale relations of mSUGRA. An observation of B(s)-->mu(+)mu(-) at the Tevatron implies a mass of the lightest SUSY Higgs boson below 120 GeV. B(s)-->mu(+)mu(-) can also significantly probe SO(10) SUSY GUT models.