MoneyGram wired transfer implemented many changes to its technology platforms designed to prevent or detect suspicious transactions. How quickly the money will reach the recipient? MoneyGram Money Order comes anywhere in the world in 10 minutes. Using the MoneyGram system, you can easily send money to your relatives and friends in other countries. What are the main benefits of money transfers by MoneyGram? Cost. Today, it is most advantageous to the customer service of all the similar services. MoneyGram hired compliance officers in many of their global offices to ensure compliance with regulations of specific countries or regions.