In the current artificial intelligence (AI) era, the scale and quality of the dataset play a crucial role in training a high-quality AI model. However, often original data cannot be shared due to privacy concerns and regulations. A potential solution is to release a synthetic dataset with a similar distribution to the private dataset. Nevertheless, in some scenarios, the attributes required to train an AI model are distributed among different parties, and the parties cannot share the local data for synthetic data construction due to privacy regulations. In PETS 2024, we recently introduced the first Vertical Federated Learning-based Generative Adversarial Network (VFLGAN) for publishing vertically partitioned static data. However, VFLGAN cannot effectively handle time-series data, presenting both temporal and attribute dimensions. In this article, we proposed VFLGAN-TS, which combines the ideas of attribute discriminator and vertical federated learning to generate synthetic time-series data in the vertically partitioned scenario. The performance of VFLGAN-TS is close to that of its counterpart, which is trained in a centralized manner and represents the upper limit for VFLGAN-TS. To further protect privacy, we apply a Gaussian mechanism to make VFLGAN-TS satisfy an $(ε,δ)$-differential privacy. Besides, we develop an enhanced privacy auditing scheme to evaluate the potential privacy breach through the framework of VFLGAN-TS and synthetic datasets.