In this Letter calculations are used to analyse the molecular dynamics of the allene molecule after removing an electron from one CH2 group, which corresponds to formation of the radical cation in its first excited state. Electron transfer (ET) is then seen to occur from one end of the molecule to the other on the femtosecond time-scale. The second excited state also plays a role, providing a vibronically mediated pathway for the transfer in addition to the direct route. Utilising recent results [Mahapatra et al., J. Phys. Chem. A 105 (2000) 5567], full quantum dynamics calculations including all 15 vibrational modes and three electronic states have been made, which provide a benchmark for studying the ET in this prototypical system.