  Electron injections are critical processes associated with magnetospheric
substorms, which deposit significant electron energy into the ionosphere.
Although wave scattering of $<$10 keV electrons during injections has been well
studied, the link between magnetotail electron injections and energetic
($\geq$100 keV) electron precipitation remains elusive. Using conjugate
observations between the ELFIN and Magnetospheric Multiscale (MMS) missions, we
present evidence of tens to hundreds of keV electron precipitation to the
ionosphere potentially driven by kinetic Alfv\'en waves (KAWs) associated with
magnetotail electron injections and magnetic field gradients. Test particle
simulations adapted to observations show that dipolarization-front magnetic
field gradients and associated $\nabla B$ drifts allow Doppler-shifted Landau
resonances between the injected electrons and KAWs, producing electron spatial
scattering across the front which results in pitch-angle decreases and
subsequent precipitation. Test particle results show that such KAW-driven
precipitation can account for ELFIN observations below $\sim$300 keV.
