There is a setting in the A/R company profile to accomodate moving Current A/R transactions to History. It will either be by 'Period End' or by 'Billing Cycle'. The former method is more obvious - run period end in AR to move completed transactions to history. The latter is less obvious - you need to print statements, and choose Yes to wanting to clear transactions on the screen that appears after printing.

Transactions are cleared based on their document dates. If a transaction has a date in the future (or after the specified clearing date), it will not be moved to history.