MoneyGram wired transfer implemented many changes to its technology platforms designed to prevent or detect suspicious transactions. The greatest increases in Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. Millions of families depend on MoneyGram to safely send money home or pay the bills. MoneyGram company operates around the clock and all 7 days a week, so the time of money transfer takes only 10 minutes.