Spin injection from epitaxial iron into InGaAs/InAs quantum wells is observed using an all-electric nonlocal setup. From the choice of material, a significant spin-orbit interaction (SOI) is expected. The contact separation of the spin-valve devices is in the order of the mean free path so that the transport is at the transition between diffusive and ballistic. With an established purely diffusive model a spin-injection efficiency of 77% is determined from the data. This value is very large compared to previous observations on diffusive spin-valve devices on similar material systems. Motivated by similar results on ballistic spin-valve devices in a material system with small spin-orbit coupling, a recent model was suggested in which a ballistic spin-dephasing length was pointed out to be the crucial length scale. With this model and an experimentally determined spin-orbit coupling parameter of α=4×10−12 eV m, very high spin-injection efficiencies are still determined in our quantum wells. We suggest that the spin-dephasing length to be used in the model must be larger due to the crystallographic anisotropy of the spin-orbit coupling, i.e., in our setup the SOI stabilizes the spin in the crystal direction of the spin-polarized current.