As I read it, he claws no cash back, because the sheik hasn't sold existing shares but instead, CFG have released additional shares which the Chinese have bought, hence the money going into CFG, not the sheik's hands
The sheik's holding is therefore diluted, but the overall entity is arguably worth more with the additional investment, hence overall a neutral move for the sheik personally from a financial perspective
As for questions from others about FFP or 'what percentage of this money belongs to city' - you are barking up the wrong tree. A holding company can choose to move that money into whichever subsidiaries it wishes, be it all to Manchester city, all to NY, split across several, create a new subsidiary, keep it at group level, etc.