In this paper, we demonstrate that a neural decoder trained on neural activity signals of one subject can be used to \textit{robustly} decode the motor intentions of a different subject with high reliability. This is achieved in spite of the non-stationary nature of neural activity signals and the subject-specific variations of the recording conditions. Our proposed algorithm for cross-subject mapping of neural activity is based on deep conditional generative models. We verify the results on an experimental data set in which two macaque monkeys perform memory-guided visual saccades to one of eight target locations.