Hello, and welcome to what's left of the forum! It's always great to see someone getting back into these great games! I remember having similar problems with this one too. You have to go into the LP III folder, then into the "Patch_LP2_to_LP3" subfolder. You have to follow all of the steps carefully.
You must transfer the "FaceSet" folder there into the main LPIII folder, then transfer the map file to the LPII folder. Then, start your last LPII save before the lab, complete the last quest, and you will be given a chance to save. Quit the game immediately after saving, and transfer that save file directly to the LPIII folder, and you should be good to go. Just be careful, as a lot of taught spells don't transfer properly, and you might end up losing them! Hope this helps!
Also, I just recently released my full walkthrough of the game, so if you ever get stuck or think you might have missed something, please give it a look! Have a great day, and I hope you enjoy the game once again!