Thanks to the fast progress in synthetic media generation, creating realistic false images has become very easy. Such images can be used to wrap "rich" fake news with enhanced credibility, spawning a new wave of high-impact, high-risk misinformation campaigns. Therefore, there is a fast-growing interest in reliable detectors of manipulated media. The most powerful detectors, to date, rely on the subtle traces left by any device on all images acquired by it. In particular, due to proprietary in-camera processes, like demosaicing or compression, each camera model leaves trademark traces that can be exploited for forensic analyses. The absence or distortion of such traces in the target image is a strong hint of manipulation. In this paper, we challenge such detectors to gain better insight into their vulnerabilities. This is an important study in order to build better forgery detectors able to face malicious attacks. Our proposal consists of a GAN-based approach that injects camera traces into synthetic images. Given a GAN-generated image, we insert the traces of a specific camera model into it and deceive state-of-the-art detectors into believing the image was acquired by that model. Likewise, we deceive independent detectors of synthetic GAN images into believing the image is real. Experiments prove the effectiveness of the proposed method in a wide array of conditions. Moreover, no prior information on the attacked detectors is needed, but only sample images from the target camera.