If MoneyGram money transfer, for some reason has not been received by the addressee, the sender will receive a refund. Understanding that being in another country, you may not be fluent in the local language, that's why MoneyGram always tries to talk to you in your native language. MoneyGram - is an urgent money transfer by means of wired transfer around the world without opening a bank account. MoneyGram International, Inc. - The U.S. financial company engaged in operations in the international financial markets since 1940. MoneyGram completed the rollout of simplified pricing for money transfer services in the U.S., an initiative that began last year.