SpaceX, the rocket and satellite maker led by Elon Musk, said on Monday it had acquired xAI, the artificial intelligence company controlled by Mr. Musk, a sweeping move to consolidate his business empire as it faces questions about the cost of its A.I. ambitions.

In emails dating to 2012, the Tesla and SpaceX CEO and the millionaire financier discussed holiday plans, parties, SpaceX visits and lack of sleep.