The greatest increases in Technology continues to play a key role in increasing MoneyGram transaction speed, automating and streamlining processes, and creating new functionality. The company continues to automate and enhance MoneyGram How quickly the money will reach the recipient? MoneyGram Money Order comes anywhere in the world in 10 minutes. MoneyGram launched a new in-person bill payment service which will be delivered through agents in their domestic network, giving consumers an easy, low-cost method to pay their bills. The benefits of money transfers by MoneyGram: high-speed delivery of transfers (10-15 min).