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We propose several novel scenarios how capture of small sublunar-mass primordial black holes (PBHs) by compact stars, white dwarfs or neutron stars, can lead to distinct short gamma-ray bursts (sGRBs) as well as microquasars (MQs). In addition to providing new signatures, relativistic jets from these systems will accelerate positrons to high energies. We find that if PBHs constitute a sizable fraction of DM, they can significantly contribute to the excess observed in the positron flux by the Pamela, the AMS-02 and the Fermi-LAT experiments. Our proposal combines the beneficial features of astrophysical sources and dark matter.