Aside from a comment on the "labour socially necessary" in Engels's preface, there is no other mention of socially necessary labour time in volume II of Capital. That preface is where Engels wrote of Marx saving The Source and Remedy from oblivion, albeit with only a single, short innocuous quotation (see also this earlier post).
In the early post, I related how Anton Menger had doubted Engels's story of the pamphlet's influence on Marx. Menger's book was first published in German in 1886, long before Marx's notebooks from 1857-58 and 1861-63 were published. The evidence in those notebooks is that the pamphlet's influence on Marx was greater than Engels had claimed. Because I have already discussed the "saved from oblivion" passage, I will say no more at this time.
The passage from the preface that mentioned labour socially necessary is of interest because it appears in an argument Engels was making about Marx's scientific originality.
Marx stands in the same relation to his predecessors in the theory of surplus-value as Lavoisier stood to Priestley and Scheele. The existence of that part of the value of products which we now call surplus-value had been ascertained long before Marx. It had also been stated with more or less precision what it consisted of, namely, of the product of the labour for which its appropriator had not given any equivalent. But one did not get any further. Some — the classical bourgeois economists — investigated at most the proportion in which the product of labour was divided between the labourer and the owner of the means of production. Others — the Socialists — found that this division was unjust and looked for utopian means of abolishing this injustice. They all remained prisoners of the economic categories as they had come down to them.
Now Marx appeared upon the scene. And he took a view directly opposite to that of all his predecessors. What they had regarded as a solution, he considered but a problem.
Granted, Marx's solution was impressive and original. But Engels overestimated the extent to which Marx's predecessors "remained prisoners of the economic categories as they had come down to them." The "Ricardian Socialists" were neither Ricardian nor socialist. Even if Menger was wrong about the 1821 pamphlet's influence on Marx, he was right about the debt of the pamphleteers to William Godwin's Political Justice.
The first of two points on which "the Ricardian school suffered shipwreck," according to Engels, was the apparent paradox between the value of the wage and the value of the product of labour. Marx's solution was to distinguish between labour and labour-power, the latter being the commodity the worker sells:
It is not labour which is bought and sold as a commodity, but labour-power. As soon as labour-power becomes a commodity, its value is determined by the labour embodied in this commodity as a social product. This value is equal to the labour socially necessary for the production and reproduction of this commodity. Hence the purchase and sale of labour-power on the basis of its value thus defined does not at all contradict the economic law of value.
Engels here elided the possibility that labour power may not sell at its value or may be unsaleable, a point also omitted by Marx in chapter six of volume one.