If MoneyGram money transfer, for some reason has not been received by the addressee, the sender will receive a refund. Technology continues to play a key role in increasing MoneyGram transaction speed, automating and streamlining processes, and creating new functionality. How quickly the money will reach the recipient? MoneyGram Money Order comes anywhere in the world in 10 minutes. MoneyGram - is an urgent money transfer by means of wired transfer around the world without opening a bank account. MoneyGram International, one of the leading companies in the global money transfer market, has announced that its customers in Israel can now send and receive money transfers in Euro.