The correct answer to this open question is the following.
To what extent did Stephen F. Austin succeed or fail at continuing the dreams of his father?
I consider that Stephen F. Austin succeeded at continuing his fathers' dream of colonizing the region of Texas.
After the death of his father Moses, Stephen Fuller Austin (1793-1836) committed himself to the venture of colonizing the region of Texas. He had shown skills to be a good leader and business since he had studied in New Orleans. So Stephen was true to the wishes of his father and continued with the project of the colonization of Texas. Once the family had the approval of the Spanish governor, Stephen started to take Americans to Texas in 1821. After Mexico won the War of Independence against the Spanish crown Stephen had to travel to México to negotiate with the Mexican authorities to respect the grant given by the Spanish governor. He succeeded and successfully proceeded with colonization.