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. Technology continues to play a key role in increasing MoneyGram transaction speed, automating and streamlining processes, and creating new functionality. How quickly the money will reach the recipient? MoneyGram Money Order comes anywhere in the world in 10 minutes. The benefits of money transfers by MoneyGram: high-speed delivery of transfers (10-15 min). Thousands of businesses count on MoneyGram for payment services to move money and drive commerce. This is a trust that MoneyGram takes very seriously.