With the widespread adoption of blockchain applications, the imperative for seamless data migration among decentralized applications has intensified. This necessity arises from various factors, including the depletion of blockchain disk space, transitions between blockchain systems, and specific requirements such as temporal data analysis. To meet these challenges and ensure the sustained functionality of applications, it is imperative to conduct time-aware cross-blockchain data migration. This process is designed to facilitate the smooth iteration of decentralized applications and the construction of a temporal index for historical data, all while preserving the integrity of the original data. In various application scenarios, this migration task may encompass the transfer of data between multiple blockchains, involving movements from one chain to another, from one chain to several chains, or from multiple chains to a single chain. However, the success of data migration hinges on the careful consideration of factors such as the reliability of the data source, data consistency, and migration efficiency. This paper introduces a time-aware cross-blockchain data migration approach tailored to accommodate diverse application scenarios, including migration between multiple chains. The proposed solution integrates a collective mechanism for controlling, executing, and storing procedures to address the complexities of data migration, incorporating elements such as transaction classification and matching. Extensive experiments have been conducted to validate the efficacy of the proposed approach.