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. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. MoneyGram completed the rollout of simplified pricing for money transfer services in the U.S., an initiative that began last year. The benefits of money transfers by MoneyGram: sender of of transfer can choose to receive a money transfer currency - U.S. dollars or euros.