Don’t have a source for now, it is just based on my basic understanding of the tax laws.
Hope you agree that the non-relative will have to pay a gift tax.
If that is agreed, then we would have decided on what amount they have to pay the tax on.
The market value of the security on the date of gift will be that amount, if I am gifting shares worth ₹10 lacs, then the donee would pay tax on the ₹10 lacs.
Since the donee already paid tax on the 10 lacs, it would in turn become his cost of acquisition, and from then on, tax needs to be paid only on the future capital gains with 10 lacs being the cost of acquisition.