If you're using a flash drive (or a hard drive, or any kind of storage really) plug it into your PC. Go to Aeria folder. Copy it. Move it to the drive. Unplug the drive when it's done copying. Plug it in your new PC. Move the newly copied Aeria folder.
It's really that simple
And I think all you should do is install the game, which doesn't require much.
Another solution (the long one) is to download it and pause when it's halfway done. Continue it later so that the internet doesn't get worse.. this is what I personally did when I needed to download big games.