That sounds backwards on both points. Poverty impacts how people perceive and interact with the world from building relationships to the use and conservation of assets. For example people in poverty are less likely to save for the future because institutions necessary to safely preserve assets into the future are distant therefore resulting in behaviors motivated towards immediate consumption. That is not something fixed by just throwing money at it.

At the same time social systemic unfair treatment can be fixed with money as it allows an otherwise well positioned person to alter their relationship with the constraints imposing such unfair conditions.

> So, if a poor white family is given a lot of money and they move into a richer neighbourhood, they would enjoy a social capital the same amount of money cannot buy for a black family.

That imposes a bunch of unstated assumptions that may or may not apply. Most all my neighbors are black families of different economic statuses who moved into a predominately white neighborhood and did just fine regarding social capital.