The Artemis II mission has taken its four astronauts further into space than anyone has been before.
The company’s public stock debut is set to be one of the most valuable in history, and could make Musk the world's first trillionaire.
Reports it plans the biggest listing ever sent the shares of firms in its orbit soaring in US trade on Wednesday.
Musk's AI chatbot has created millions of fake sexualised images, experts say.
The crew blasted off from Cape Canaveral in a SpaceX Dragon spacecraft atop a Falcon 9 rocket.
Watch moment Falcon 9 rocket blasts off to International Space Station
Musk says the combined firm - which has been valued at more than $1tn - will be an "innovation engine".
Starlink-enabled drones have been linked to a number of recent deadly attacks by Russia on Ukraine.
The firm wants to create a network of "orbital data centres" to power artificial intelligence.