Expanding my collection

Helloooo my friends, im sure its been asked before but id like an up to date answer. When I find an abandoned ship and have the option to claim it or trade it, where does it actually go when I claim it? I dont have a freighter yet as im still in my first couple of days of playing. Can I claim it then just go about my day and the wreck will be on my freighter when I get it? And continue flying around in my current ship?