If you need to cancel or change a transaction, then you should contact by telephone with the MoneyGram branch agent, made the transaction for you. Technology continues to play a key role in increasing MoneyGram transaction speed, automating and streamlining processes, and creating new functionality. What are the main benefits of money transfers by MoneyGram? Reliability - the international payment system gives complete assurance that the money will be paid to the recipient. The benefits of money transfers by MoneyGram: simplicity in making up. MoneyGram financial results were driven by money transfer business, which delivered more than 40 percent growth in transaction volume.