  We show that at any given time, the Galactocentric black hole Sgr A* is
expected to be microlensing N(lens)=1.7 bulge stars if the threshold of
detectability of the fainter image is K(thr)=21, and about N(lens)=8 sources if
K(thr)=23. The lensed images then provide a unique way to detect stellar-mass
black holes predicted to cluster around Sgr A*. If a black hole passes close to
a microlensed image, it will give rise to a short (weeks long) microlensing
event. We show that the mass and projected velocity of the stellar-mass black
hole can both be measured unambiguously from such an event, provided that
either a caustic crossing is observed or the astrometric displacement is
measured. For K(thr)=23 and moderate magnifications by Sgr A*, the microlensing
event rate from a cluster of 20000 black holes within a radius of 0.7 pc is
only 0.06 events per year; however, if highly magnified images of a star were
found, the rate of events by the stellar black holes would be much higher. In
addition, the N(lens) sources lensed by Sgr A* provide a unique probe of
extinction behind the Galactic center along 2N(lens) lines of sight.
