Money transfers can be claimed within 45 days, but if for some reason, this period is exceeded, the processing operator would need additional time to call the main office of the company of MoneyGram for voice authorization. Technology continues to play a key role in increasing MoneyGram transaction speed, automating and streamlining processes, and creating new functionality. MoneyGram International, Inc. - The U.S. financial company engaged in operations in the international financial markets since 1940. Millions of families depend on MoneyGram to safely send money home or pay the bills.