As of my last knowledge update in January 2022, SpaceX manufactures many of the key components for its Falcon Heavy booster in-house. This includes the Merlin engines, grid fins, and fairings. Merlin engines are designed and produced by SpaceX for use on the Falcon 9 and Falcon Heavy rockets. Grid fins are also developed and manufactured by SpaceX and play a crucial role in the controlled descent of the Falcon rocket stages for reuse. Fairings, which protect payloads during the rocket's ascent through the Earth's atmosphere, are also produced by SpaceX.
It's worth noting that manufacturing processes and supply chain arrangements can change over time, so it's advisable to check the latest information from official sources or SpaceX's announcements for the most up-to-date details on the production of specific components for the Falcon Heavy booster.