This paper examines the use of Large Language Models (LLMs) for the intralingual translation of documents from standard German to German Easy Language (Leichte Sprache). We use open-weight models, from the Llama 3 family, with less than ten billion parameters. Additionally, we employ parameter-efficient fine-tuning (QLoRA) to adapt the LLMs to the requirements of Easy Language. For this purpose, we introduce a new data set (ELGEPA) (Source code to obtain the dataset: github.com/minds-hh/ger-gov-easy-lang ), which is a parallel corpus of governmental documents in standard German and Easy Language with additional metadata, obtained from all German federal states and their capitals In our experiments, a fine-tuned Llama 3.1-8B-Instruct model achieved a SARI score of 41 and Flesch Reading Ease of 69. Outperforming GPT-4o and indicating that this type of model can deliver promising text quality in Easy Language.