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 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. For the company MoneyGram is important not only to provide customers with an easy and convenient way to carry out money transfers and support their families at home, but also to help them as much as possible to adapt to the foreign countries. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc.