If the Nobel Foundation endorses a prize in his honor, then you can call it a prize in his honor, that doesn't mean you can call it a Nobel Prize. No Swede, nor any reputable newspaper or the Nobel Foundation would ever call it a Nobel Prize since it has never been recognized as one by the foundation, why would we call it that on HN?

The family actually protested pretty much immediately, not knowing that Sveriges Riksbank was trying to make another Nobel. That's why the name 'Nobel' was stripped from the prize in 1971 while it was working it's way through the court system.

So no, the Nobel family isn't going to approve another because they didn't really approve of this one and aren't likely to sign anything anymore that's trying to sneak one in.