He co-founded the Manchester and Salford Boys' and Girls' Refuges and Homes in 1870, which today continues as the children's charity the Together Trust.
Here Leonard commenced his business life in one of the large Manchester warehouses where he stayed for the next thirty years, eventually becoming a manager.
A deeply religious man, he had become responsible for the Young Men's Sunday Class at St. Ann's Church in Manchester and later a Teacher at the Ragged School there.
On 4 January 1871 he and Richard Bramwell Taylor started the Manchester and Salford Boys' and Girls' Refuges and Homes in a small house on Quay Street, Deansgate.
A memorial fund was set up to raise £10,000 for two projects that Shaw had taken a special interest in; a new recreation ground in Cheetham and the enlargement of "Bethesda", a home for children with disabilities.