Sept 22 (Reuters) - SoftBank Group"s (9984.T) Vision Fund had invested in a $2.5 billion private equity fund set up by former U.S. Treasury secretary Steven Mnuchin, the Financial Times reported. Mnuchin"s Liberty Strategic Capital, which was launched earlier this year, recently raised funds from sovereign wealth funds in the Middle East including Saudi Arabia"s Public Investment Fund, the report said on Wednesday.