If this is a true gift, that is, not part of any larger transaction and given out of the kindness of your heart, then you're probably going to have to consult a tax professional because this will depend on the precise tax treaties between the United States and India.
Generally, when you give a gift to another person in the United States, you do not have to recognize the appreciation in value of that gift as a capital gain and the recipient gets the same basis you had, so they will have to pay capital gains tax when/if they sell it.
But generally, when you give a gift to someone who is not a US citizen, you do have to recognize the appreciation of the value of the gift as a taxable capital gain before you can gift it. However, this can be modified by tax treaties.
If this is not a true gift and is part of some other kind of transaction, then you absolutely must recognize the change in value of the bitcoin as a capital gain before you can give it to someone else, domestic or foreign.
You asked:
Even if they know it was sold, how can they tax me as I am not the person who sold it?
The tax is not on the sale, it's on the increase in value which is a form of income. Generally, whenever you dispose of an asset, any increase in its value is a taxable gain. There are exceptions, such as a true domestic gift, those made by international treaty, and if it's transferred because of your death.
1Is this a true gift? That is, you aren't getting any benefit from it and are just giving it to him out of generosity? It's not part of any transaction? Did you make any other gifts to the same person this taxable year? If so, are you married? (If not, it doesn't matter.) – David Schwartz – 2018-01-24T19:05:24.253