Money transfer system Coinstar Money Transfer is the fastest growing company in the market of remittances. Money transfer system Coinstar Money Transfer is a fast-growing company in the market of remittances. Coinstar Money Transfer System works via the Internet, as opposed to Western Union and MoneyGram, which for the money transfers information are using their own internal networks. Money transfers via Coinstar Money Transfer are made in U.S. dollars and Euro, without opening an account to the Client. Until June 1, 2007 the system of "Coinstar Money Transfer" was called "Travelex Money Transfer".