NRI sponsership

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Currently, I'm on H1 B Visa & my uncle's son (mom's brother''s son) need NRI sponsership for his further education after 12 th. My cousin wants to get in MBBS/BDS & he needs sponsership for admision. Now the question is,

Does H1B holder can give NRI sponsership or not?

Does it affect greencard process ? Does it help for annual tax return?

I will appreciate if someone can reply, soon.