A good presentation of a transfer function (tf) is here http://stats.stackexchange.com/questions/124533/transfer-function-in-forecasting-models-interpretation and alternatively here http://en.wikipedia.org/wiki/Distributed_lag . Since we both have a Y and 1 X for simplicity sake then I believe that one can form a tf with appropriate assumed lags and  appropriate assumed differences of these two series that would match the assumed ECM illustrating that the ECM is a particular constrained subset of a tf model. Perhaps some other readers ( heavy econometricians ) have already gone thought the proof/algebra but I will consider your positive suggestion in helping other readers.