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Cross-Domain Recommendation (CDR) has been popularly studied to utilize different domain knowledge to solve the cold-start problem in recommender systems. Most of the existing CDR models assume that both the source and target domains share the same overlapped user set for knowledge transfer. However, only few proportion of users simultaneously activate on both the source and target domains in practical CDR tasks. In this paper, we focus on the Partially Overlapped Cross-Domain Recommendation (POCDR) problem, that is, how to leverage the information of both the overlapped and non-overlapped users to improve recommendation performance. Existing approaches cannot fully utilize the useful knowledge behind the non-overlapped users across domains, which limits the model performance when the majority of users turn out to be non-overlapped. To address this issue, we propose an end-to-end dual-autoencoder with Variational Domain-invariant Embedding Alignment (VDEA) model, a cross-domain recommendation framework for the POCDR problem, which utilizes dual variational autoencoders with both local and global embedding alignment for exploiting domain-invariant user embedding. VDEA first adopts variational inference to capture collaborative user preferences, and then utilizes Gromov-Wasserstein distribution co-clustering optimal transport to cluster the users with similar rating interaction behaviors. Our empirical studies on Douban and Amazon datasets demonstrate that VDEA significantly outperforms the state-of-the-art models, especially under the POCDR setting.