A person does not become more free because he has more wealth; he becomes wealthier, which confers on him more opportunities to use the liberty that he has.
Not necessarily. Granted, if one lives in a resource-poor society (or a desert island) then one may suffer purely from a lack of capability, rather than from imposed coercion. But in a wealthy society like ours, no individual lacks the physical or material capacity to meet their needs. There are plenty of resources nearby, sitting in shop windows. Anyone is capable of taking those resources. Their problem is that other people in society won't let them. Security guards will interfere, using force to block the individual's access, or to reclaim what they now call "stolen" goods. Money is a ticket that stops others from barring your access to society's wealth. For example, it can be used to stop the security guards from impeding your liberty when you want to claim the resources in shops. If you lack money, you lack the means to stave off their coercion. That is, you lack negative freedom.
As G.A. Cohen put it, in what I think may be the most insightful paragraph of political theory ever written:
[T]o lack money is to be liable to interference, and the assimilation of money to physical, or even mental, resources is a piece of unthinking fetishism, in the good old Marxist sense that it misrepresents social relations of constraint as people lacking things. In a word: money is no object.