  Quantum vortices are the quantized version of classical vortices. Their
center is a phase singularity or vortex core around which the flow of particles
as a whole circulates and is typical in superfluids, condensates and optical
fields. However, the exploration of the motion of the phase singularities in
coherently-coupled systems is still underway. We theoretically analyze the
propagation of an interference dislocation in the regime of strong coupling
between light and matter, with strong mass imbalance, corresponding to the case
of microcavity exciton-polaritons. To this end, we utilize combinations of
vortex and tightly focused Gaussian beams, which are introduced through
resonant pulsed pumping. We show that a dislocation originates from
self-interference fringes, due to the non-parabolic dispersion of polaritons
combined with moving Rabi-oscillating vortices. The morphology of singularities
is analyzed in the Poincar\'{e} space for the pseudospin associated to the
polariton states. The resulting beam carries orbital angular momentum with
decaying oscillations due to the loss of overlap between the normal modes of
the polariton system.
