If MoneyGram money transfer, for some reason has not been received by the addressee, the sender will receive a refund. For the recipient MoneyGram service of wired transfer is free. All expenses will be paid by the sender at the time of sending money. MoneyGram launched a new in-person bill payment service which will be delivered through agents in their domestic network, giving consumers an easy, low-cost method to pay their bills. The benefits of money transfers by MoneyGram: simplicity in making up. MoneyGram completed the rollout of simplified pricing for money transfer services in the U.S., an initiative that began last year.