Once you reach the Anomaly in the expedition, you can go to the expedition terminal and copy your most recently active ship and active multitool from your main save. If you want to copy a different ship or MT, switch back to your main save, call in the ship or activate the multitool you want, and then switch back to the expedition. You will then be able to copy that ship or multitool to your expedition save, at the cost of 1000–2000 nanites.

You can also copy multiple ships or multitools from main save to expedition this way. Copy the ship/MT to expedition, switch to main save, change the active ship/MT, switch back to expedition, and copy that one over too. I copied both my scanning MT and my battle MT this way.

When you transfer a ship, all of the installed tech comes with it, but none of the inventory.