We introduce SQL-Exchange, a framework for mapping SQL queries across different database schemas by preserving the source query structure while adapting domain-specific elements to align with the target schema. We investigate the conditions under which such mappings are feasible and beneficial, and examine their impact on enhancing the in-context learning performance of text-to-SQL systems as a downstream task. Our comprehensive evaluation across multiple model families and benchmark datasets---assessing structural alignment with source queries, execution validity on target databases, and semantic correctness---demonstrates that SQL-Exchange is effective across a wide range of schemas and query types. Our results further show that both in-context prompting with mapped queries and fine-tuning on mapped data consistently yield higher text-to-SQL performance than using examples drawn directly from the source schema.