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Forensic license plate recognition (FLPR) remains an open challenge in legal contexts such as criminal investigations, where unreadable license plates (LPs) need to be deciphered from highly compressed and/or low resolution footage, e.g., from surveillance cameras. In this work, we propose a side-informed Transformer architecture that embeds knowledge on the input compression level to improve recognition under strong compression. We show the effectiveness of Transformers for license plate recognition (LPR) on a low-quality real-world dataset. We also provide a synthetic dataset that includes strongly degraded, illegible LP images and analyze the impact of knowledge embedding on it. The network outperforms existing FLPR methods and standard state-of-the art image recognition models while requiring less parameters. For the severest degraded images, we can improve recognition by up to 8.9 percent points.