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. The company continues to automate and enhance MoneyGram Very intensive and focused approach has helped MoneyGram to grow business at a rapid pace and establish MoneyGram as a global player in the marketplace. Using the MoneyGram system, you can easily send money to your relatives and friends in other countries. What are the main benefits of money transfers by MoneyGram? Cost. Today, it is most advantageous to the customer service of all the similar services. MoneyGram completed the rollout of simplified pricing for money transfer services in the U.S., an initiative that began last year.