Marx considered his theory of money to be one of his main accomplishments and a significant advance over Ricardo’s theory and classical economics in general, which had simply taken money for granted, or explained the existence of money in ad hoc fashion, on the basis of the practical difficulties of barter, unrelated to any theory of value.

«Now, however, we have to perform a task never even attempted by bourgeois economics. That is, we have to show the origin of this money-form, we have to trace the development of the expression of value contained in the value-relation of commodities from its simplest, almost imperceptible outline to the dazzling money-form. When this has been done, the mystery of money will immediately disappear.»
(Marx 1867, p. 139; emphasis added)

According to my interpretation of Marx’s theory of money, Marx derived the necessity of money in a commodity (or market) economy from his fundamental assumption of the labor theory of value, in the crucial but often neglected Section 3 of Chapter 1 of Volume 1 of Capital.

Money Intro