MoneyGram wired transfer implemented many changes to its technology platforms designed to prevent or detect suspicious transactions. At the heart of MoneyGram is trust and reliability of customers. You can quickly send and receive money, as money transfers usually come to the recipient within 10 minutes. The benefits of money transfers by MoneyGram: the opportunity to send a telegram with money transfer (up to 10 words) for free. Millions of families depend on MoneyGram to safely send money home or pay the bills. MoneyGram completed the rollout of simplified pricing for money transfer services in the U.S., an initiative that began last year.