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Electronic Health Records (EHRs) provide crucial information for clinical decision-making. However, their high-dimensionality, heterogeneity, and sparsity make clinical prediction challenging. Large Language Models (LLMs) allowed progress towards addressing this challenge by leveraging parametric medical knowledge to enhance EHR data for clinical prediction tasks. Despite the significant achievements made so far, most of the existing approaches are fundamentally task-agnostic in the sense that they deploy LLMs as EHR encoders or EHR completion modules without fully integrating signals from the prediction tasks. This naturally hinders task performance accuracy. In this work, we propose Rewrite-To-Predict (ReToP), an LLM-based framework that addresses this limitation through an end-to-end training of an EHR rewriter and a clinical predictor. To cope with the lack of EHR rewrite training data, we generate synthetic pseudo-labels using clinical-driven feature selection strategies to create diverse patient rewrites for fine-tuning the EHR rewriter. ReToP aligns the rewriter with prediction objectives using a novel Classifier Supervised Contribution (CSC) score that enables the EHR rewriter to generate clinically relevant rewrites that directly enhance prediction. Our ReToP framework surpasses strong baseline models across three clinical tasks on MIMIC-IV. Moreover, the analysis of ReToP shows its generalizability to unseen datasets and tasks with minimal fine-tuning while preserving faithful rewrites and emphasizing task-relevant predictive features.