These cards use the same back with his cards but I realized his cards show as Death Star Plans when they are hidden in a player's hand, while mine show as their corresponding card back.

I don't want to simply take his cards, change it and put it into my mod (if he wants to he can take mine), but you can fix it in 15 seconds yourself.

Just right click on one of the objective decks, choose "Custom". There will be an option saying "Back is Hidden" in the bottom, tick it and click "Import". Do it for other decks too and you are done.