You can't pray over someone who already died on kufr. This article and many responses reiterate [9:113] and [9:84]. The last prophet (pbuh) not being allowed to pray for Abu Talib is a pretty big deal and should give you red flags if you're trying to argue against this.

On the other hand, Janazah is obligatory if you know that someone died in Islam. You must do it. So if you're of the opinion that Hawking died muslim, then please ask his family/caretakers to allow you for janazah. If you're not allowed, organize a janazah in absentia. Pls let us know tomorrow how that goes.

If you're in the middle, quit bickering against a teacher of Islam trying to teach people Islam using current contexts.