  The discovery of gravitational waves from binary black hole mergers has
renewed interest in primordial black holes forming a part of the dark matter
density of our Universe. Various tests have been proposed to test this
hypothesis. One of the cleanest tests is the lensing of fast radio bursts. In
this situation, the presence of a compact object near the line of sight
produces two images of the radio burst. If the images are sufficiently
separated in time, this technique can constrain the presence of primordial
black holes. One can also try to detect the lensed image of the mini-bursts
within the main burst. We show that this technique can produce the leading
constraints over a wide range in lens masses $\gtrsim$ 2 $M_\odot$ if the
primordial black holes follow a single mass distribution. Even if the
primordial black holes have an extended mass distribution, the constraints that
can be derived from lensing of fast radio bursts will be the most constraining
over wide ranges of the parameter space. We show that this technique can probe
exotic compact boson stars and fermion stars made up of beyond the Standard
Model particles. This search strategy is competitive and can provide the
leading constraints on parts of the particle physics parameter space when
compared with gravitational wave observations.
