Since you now have to log into an Intuit Account when you first install it, all your downloads and licenses are listed there (even if you bought it from somewhere else) so if you need to install it again or install on another computer, even on the other operating system (Windows, Mac) you can download it again here,
https://accounts.intuit.com/app/account-manager/productsBilling/turbotax
For Windows…..What I would do on the old computer, is copy the whole Turbo Tax folder that is under your Documents. That should be where the .tax files and pdf files are stored. Also if you haven't done it, I would open each year in the program and save it as a pdf file, go to FILE - SAVE TO PDF so you don't need the program installed to view your return. Copy that folder to a flash drive or best yet is to burn it to a CD or DVD and then you will have a backup of them. Then on the new computer copy the folder (or files) from the flash drive to your Documents folder.