Solar-mass black holes with masses in the range of $sim 1-2.5 M_{odot}$ are not expected from conventional stellar evolution, but can be produced naturally via neutron star (NS) implosions induced by capture of small primordial black holes (PBHs) or from accumulation of some varieties of particle dark matter. We argue that a unique signature of such transmuted solar-mass BHs is that their mass distribution would follow that of the NSs. This would be distinct from the mass function of black holes in the solar-mass range predicted either by conventional stellar evolution or early Universe PBH production. We propose that analysis of the solar-mass BH population mass distribution in a narrow mass window of $sim 1-2.5,{rm M}_odot$ can provide a simple yet powerful test of the origin of these BHs. Recent LIGO/VIRGO gravitational wave (GW) observations of the binary merger events GW190425 and GW190814 are consistent with a BH mass in the range $sim 1.5-2.6~M_{odot}$. Though these results have fueled speculation on dark matter-transmuted solar-mass BHs, we demonstrate that it is unlikely that the origin of these particular events stems from NS implosions. Data from upcoming GW observations will be able to distinguish between solar-mass BHs and NSs with high confidence. This capability will facilitate and enhance the efficacy of our proposed test.