  Experimental searches for the electron electric dipole moment (EDM) probe new
physics beyond the Standard Model. The current best EDM limit was set by the
ACME Collaboration [Science \textbf{343}, 269 (2014)], constraining time
reversal symmetry ($T$) violating physics at the TeV energy scale. ACME used
optical pumping to prepare a coherent superposition of ThO $H^3\Delta_1$ states
that have aligned electron spins. Spin precession due to the molecule's
internal electric field was measured to extract the EDM. We report here on an
improved method for preparing this spin-aligned state of the electron by using
STIRAP. We demonstrate a transfer efficiency of $75\pm5\%$, representing a
significant gain in signal for a next generation EDM experiment. We discuss the
particularities of implementing STIRAP in systems such as ours, where molecular
ensembles with large phase-space distributions are transfered via weak
molecular transitions with limited laser power and limited optical access.
