If I buy some bitcoin worth $1K, including fee and cost, then one year later it is worth $2K. At that time, I give it to my friend. My friend then sells it for $2K. Then, does my friend have to pay tax?
First of all you need to tell the country in which you are residing and doing this transaction. If it's the US please tell the state too as taxes differ for each state. But yes one thing is constant which I have seen in the tax laws of a lot of countries. In case of such a transaction either the gift that you have made is taxed at its Fair Market Value in hands of your Friend at the time of receipt, it's not a gift but a sort of income for him. So he would end up paying tax on receiving and then will pay tax when he sells it(If he sells for profit) but this time the profit will be the
amount of sale minus the
fair value at time of the gift.
Some countries practice a different system. In those countries when your friend sells the bitcoin ultimately, he will be taxed on profits and in this case, the purchase price will be taken as a difference between sale proceeds and
your purchase value(In this case which is $1K).
So in my opinion Either ways you will end up paying tax.