We present a method for creating parallel data to train Seq2Seq neural networks for sentiment transfer. Most systems for this task, which can be viewed as monolingual machine translation (MT), have relied on unsupervised methods, such as Generative Adversarial Networks (GANs)-inspired approaches, for coping with the lack of parallel corpora. Given that the literature shows that Seq2Seq methods have been consistently outperforming unsupervised methods in MT-related tasks, in this work we exploit the use of semantic similarity computation for converting non-parallel data onto a parallel corpus. That allows us to train a transformer neural network for the sentiment transfer task, and compare its performance against unsupervised approaches. With experiments conducted on two well-known public datasets, i.e. Yelp and Amazon, we demonstrate that the proposed methodology outperforms existing unsupervised methods very consistently in fluency, and presents competitive results in terms of sentiment conversion and content preservation. We believe that this works opens up an opportunity for seq2seq neural networks to be better exploited in problems for which they have not been applied owing to the lack of parallel training data.