@Kaphotics it appears that directly dragging it into a WC slot, without viewing it then setting it, is what's causing the problem. (I was able to replicate the issue)
@DonateloGM in the mean time, there's a way for it to work.
I'm using latest PKHeX (which I download directly from here, our site).
All I did was:
1. Load the save in PKHeX
2. Drag the WC6 into the mystery gift window (and if you're skeptical, I used the exact copy you uploaded.)
3. I view the wonder card, and set it into the slot. (right click on the icon and you'll see those options)
4. Save the save as "main" using PKHeX.
5. Load up the game.
Didn't modify any events flags or anything. Literally those 5 steps.