Why can the Babylonian kingdom be called the successor of the Sumerian?

There are several reasons for this. First, the Babylonian kingdom was located in the territory where the Sumerians once lived. Second, the Babylonians borrowed the culture of their predecessors. The Babylonians themselves were a mixture of Amorites, Sumerians and Akkadians. The Babylonian kingdom, as you know, was formed at the beginning of the 2nd millennium BC. It flourished during the reign of King Hammurabi (1792-1750 BC).