If MoneyGram money transfer, for some reason has not been received by the addressee, the sender will receive a refund. In due time MoneyGram separated from the Western Union and became an independent brand. AgentConnect continues to be an attractive alternative for businesses that choose to integrate their networks and point-of-sale platforms with the MoneyGram wired transfer. What are the main benefits of money transfers by MoneyGram? Individual flexible service. The recipient has the opportunity to receive money at any MoneyGram office anywhere in the world. MoneyGram completed the rollout of simplified pricing for money transfer services in the U.S., an initiative that began last year.