Presentation Attack Detection (PAD) systems are usually designed independently of the fingerprint verification system. While this can be acceptable for use cases where specific user templates are not predetermined, it represents a missed opportunity to enhance security in scenarios where integrating PAD with the fingerprint verification system could significantly leverage users' templates, which are the real target of a potential presentation attack. This does not mean that a PAD should be specifically designed for such users; that would imply the availability of many enrolled users' PAI and, consequently, complexity, time, and cost increase. On the contrary, we propose to equip a basic PAD, designed according to the state of the art, with an innovative add-on module called the Closeness Binary Code (CC) module. The term "closeness" refers to a peculiar property of the bona fide-related features: in an Euclidean feature space, genuine fingerprints tend to cluster in a specific pattern. First, samples from the same finger are close to each other, then samples from other fingers of the same user and finally, samples from fingers of other users. This property is statistically verified in our previous publication, and further confirmed in this paper. It is independent of the user population and the feature set class, which can be handcrafted or deep network-based (embeddings). Therefore, the add-on can be designed without the need for the targeted user samples; moreover, it exploits her/his samples' "closeness" property during the verification stage. Extensive experiments on benchmark datasets and state-of-the-art PAD methods confirm the benefits of the proposed add-on, which can be easily coupled with the main PAD module integrated into the fingerprint verification system.