I'm a personal user of Ubuntu - help me recover my data

I have an SSD with my data, rescued from a laptop that suffered a fried battery. I have the SSD mounted on an HDD slot on a desktop cage, and I can access it but I can't boot from it (no efi). I want to copy/ backup my home data, which is in it's own partition, onto a partition on my new laptop, on which I've already installed ubuntu, and be able to use it normally.

Oh, and on my new laptop my network card is disabled for some reason. I need to get that working.