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. Around the world, MoneyGram is working with leading financial institutions. The company continues to automate and enhance MoneyGram What are the main benefits of money transfers by MoneyGram? Cost. Today, it is most advantageous to the customer service of all the similar services. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. Thousands of businesses count on MoneyGram for payment services to move money and drive commerce. This is a trust that MoneyGram takes very seriously.