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. What are the main benefits of money transfers by MoneyGram? Simple - the money transfer procedure is maximally simplified. MoneyGram - is an urgent money transfer by means of wired transfer around the world without opening a bank account. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc.