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I would like to know if is a correct procedure to join training-set and validation-set together, in order to train the model on this new dataset, before making predictions on the test-set.

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Yes, once you optimized your model and parameters with the validation set, it is advised to train your final model on the combination of the training and validation sets before applying it to the test set. Indeed, you can see the validation set as a subset of the training set. It is used to tweak your models and your parameters, but once it is done, it would just be a waste to not use the validation set for training during the testing phase.

Remember that once you tested your model on the test set, you should not tweak it anymore.

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In theory, you use the training set to learn the weights, the validation set to adjust the network architecture and the testing set to verify the generalisation of your network. You can find further details on this towards data science article. Only the accuracy on the testing set - unseen during both the training and the architecture tuning - give you an unbiased idea of your performance.

If you want now to use your model on new data - in production for instance - you could re-train it on the training + validation sets.

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