Money transfers can be claimed within 45 days, but if for some reason, this period is exceeded, the processing operator would need additional time to call the main office of the company of MoneyGram for voice authorization. MoneyGram International, Inc. - The U.S. financial company engaged in operations in the international financial markets since 1940. The benefits of money transfers by MoneyGram: simplicity in making up. MoneyGram completed the rollout of simplified pricing for money transfer services in the U.S., an initiative that began last year.