Just skimming the Wikipedia article [1] and it is appears Bourdieu's argument is bit more nuanced than status and money. It is a bit laden with Marxist jargon, but at least the abstract seems to place the heavy burden on "cultural capital" which is a more precise term than what I chose (status) but close enough to my meaning.

Whether or not economic capital is actually transferrable to cultural capital seems to be another debate, but as the old saying goes "money can't buy taste". In fact, a newly rich lower class person marrying a contemporarily poor higher class person seems more likely.

As the abstract states: "Because persons are taught their cultural tastes in childhood, a person's taste in culture is internalized to their personality, and identify his or her origin in a given social class, which might or might not impede upward social mobility." Money can't rebuild the personality that is internalized in youth, but marriage might give your kids a shot.

1. https://en.wikipedia.org/wiki/Distinction_(book)

edit: also to add, the relationship between these is the underlying theme of The Great Gatsby.