In due time MoneyGram separated from the Western Union and became an independent brand. 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. MoneyGram - is an urgent money transfer by means of wired transfer around the world without opening a bank account. 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. In March 2012, the company MoneyGram merged with the network of U.S. payment centers ZipZap.