When sending the transfer via MoneyGram in one currency and receiving it in another, then currency conversion is carried out at the current rate of sales of current service point. In due time MoneyGram separated from the Western Union and became an independent brand. How to send money via MoneyGram money transfer? To make up a money transfer you should go to the MoneyGram agents and fill the application form for transfer. MoneyGram International, Inc. - The U.S. financial company engaged in operations in the international financial markets since 1940.