International company MoneyGram has expanded its service capabilities of online money transfers to UK residents. Since going public two and a half years ago, MoneyGram has made great strides by pouring energy and resources into several critically important areas for business. MoneyGram The benefits of money transfers by MoneyGram: simplicity in making up. 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.