Marx was a moralist. He held moral principles and condemned those who disregarded what was right and good. His materialist conception of history was an explanation of a world that had gone wrong, with support from political laws, but could be set right. He appealed to “the simple laws of morals and justice, which ought to govern the relations of private individuals” (Inaugural Address to the International). Some think that moralities are relative to the times and culture, but there are pitfalls in attempts at establishing different moralities. Marx did not have a theory of morality, but he took moral positions that he applied universally, even where others might apply them differently. For Marx the International would have one morality for all.
Marx, Engels, and Marxisms
Department of Philosophy

Ware, R.X. (2019). Marx’s morality for all. In Marx on Emancipation and Socialist Goals. doi:10.1007/978-3-319-97716-4_8