The benefits of money transfers by MoneyGram: high level of data protection and confidentiality of money transfers. At the heart of MoneyGram is trust and reliability of customers. You can quickly send and receive money, as money transfers usually come to the recipient within 10 minutes. MoneyGram offers an efficient, fast and secure way to send money around the world. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. The Global Funds Transfer segment is the primary segment of MoneyGram, providing money transfer and bill payment services to consumers, who are often unbanked or underbanked.