For the recipient MoneyGram service of wired transfer is free. All expenses will be paid by the sender at the time of sending money. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. The benefits of money transfers by MoneyGram: high-speed delivery of transfers (10-15 min). MoneyGram point-of-sale systems are continually upgraded to provide the latest new products and functionality. Thousands of businesses count on MoneyGram for payment services to move money and drive commerce. This is a trust that MoneyGram takes very seriously.