When someone dies, that person may have a beneficiary, like a son inheriting his father's wealth. If you inherit his business as well, that is like inheriting the effect he had on the world.

"Pulling the strings" is a puppet metaphor. The puppet represents a figurehead who does not make the real decisions. The puppeteer pulls the strings, and it looks like the puppet has agency. Using a puppet and "pulling the strings" is a way to camouflage one's actions and identity.