The greatest increases in In due time MoneyGram separated from the Western Union and became an independent brand. Experienced consultants of MoneyGram will help you in execution of documents for payment and you will be pleasantly surprised by the speed of service. 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: sender of of transfer can choose to receive a money transfer currency - U.S. dollars or euros.