Yes, it is legal and possible.
Have you copied your cards (the animations, at least) to an external hard drive?
If not, please do so.
Then, go to your new computer, move (or copy) your cards to the new computer.
Then, download and install the program to that computer.
During the install, you will see a screen showing the default location of the cards.
Make sure to change that to the actual location of your cards.
Then, finish the installation.
Wait for the program to finish finding your cards and updating them.
If all is successful, all of them will show as having been downloaded.