  We study the acceleration of electrons and positrons at an
electromagnetically modified, ultra-relativistic shock in the context of pulsar
wind nebulae (PWNe). We simulate the outflow produced by an obliquely rotating
pulsar in proximity of its termination shock with a two-fluid code which uses a
magnetic shear wave to mimic the properties of the wind. We integrate electron
trajectories in the test-particle limit in the resulting background
electromagnetic fields to analyse the injection mechanism. We find that the
shock-precursor structure energizes and reflects a sizeable fraction of
particles, which becomes available for further acceleration. We investigate the
subsequent first-order Fermi process sustained by small-scale magnetic
fluctuations with a Monte Carlo code. We find that the acceleration proceeds in
two distinct regimes: when the gyro-radius $r_{\textrm{g}}$ exceeds the
wavelength of the shear $\lambda$, the process is remarkably similar to
first-order Fermi acceleration at relativistic, parallel shocks. This regime
corresponds to a low density wind which allows the propagation of superluminal
waves. When $r_{\textrm{g}}<\lambda$, which corresponds to the scenario of
driven reconnection, the spectrum is softer.
