Climate disclosure classification is a fundamental task for analysing corporate climate disclosures, yet such disclosures appear in many different sources -- annual reports, press releases, and earnings calls -- that differ in length, purpose, and writing style. Existing evaluations are mostly conducted within a single source, leaving open whether common LLM adaptation strategies remain effective under source shift. We reframe climate disclosure classification as a cross-source adaptation problem and study three widely used adaptation strategies -- definitions, examples, and fine-tuning -- across eleven open- and closed-source LLMs, using two corpora that share the same label space but come from different sources. We find that all strategies bring positive cross-source gains on average, but the strongest in-source strategies are not the strongest cross-source ones: similarity-based retrieval and LoRA fine-tuning gain most in-source but lose most of that advantage under source shift; randomly selected few-shot examples, a weaker in-source baseline, retain their advantage more reliably; definitions transfer most consistently, though only when their granularity matches the target text. Across these strategies, when the source changes, simpler is often safer.

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