Objective. In this paper, we consider the problem of cross-subject decoding, where neural activity data collected from the prefrontal cortex of a given subject (destination) is used to decode motor intentions from the neural activity of a different subject (source). Approach. We cast the problem of neural activity mapping in a probabilistic framework where we adopt deep generative modelling. Our proposed algorithm uses deep conditional variational autoencoder to infer the representation of the neural activity of the source subject into an adequate feature space of the destination subject where neural decoding takes place. Results. We verify our approach on an experimental data set in which two macaque monkeys perform memory-guided visual saccades to one of eight target locations. The results show a peak cross-subject decoding improvement of $8\%$ over subject-specific decoding. Conclusion. We demonstrate that a neural decoder trained on neural activity signals of one subject can be used to 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. Significance. The findings reported in this paper are an important step towards the development of cross-subject brain-computer that generalize well across a population.