  Primordial black holes, which could have formed during the early Universe
through overdensities in primordial density fluctuations during inflation, are
potential candidates for dark matter. We explore the use of lensing parallax of
Gamma ray bursts (GRBs), which results in different fluxes being observed from
two different vantage points, in order to probe the abundance of primordial
black holes in the unexplored window within the mass range
$[10^{-15}-10^{-11}]M_\odot$. We derive the optical depth for the lensing of
GRBs with a distribution of source properties and realistic detector
sensitivities. We comment on the ability of the proposed Indian twin satellite
mission Daksha in its low earth orbit to conduct this experiment. If the two
Daksha satellites observe 10000 GRBs simultaneously and the entirety of dark
matter is made up of $[10^{-15}-10^{-12}]M_\odot$ black holes, Daksha will
detect non-zero lensing events with a probability ranging from 80 to 50 per
cent at the bin edges, respectively. Non-detections will not conclusively rule
out primordial black holes as dark matter in this mass range. However, we show
that meaningful constraints can be obtained in such a case if the two
satellites are separated by at least the Earth-Moon distance.
