Yes. Your friend must pay tax on any capital gains. In this simple case, the basis for them is your cost.
https://www.irs.gov/faqs/capital-gains-losses-and-sale-of-home#collapse-6
This is correct for the US. I'll add that the amount of capital gains tax depends on your friend's income/tax bracket and could be 0 at the federal level if their income is low enough. If your income was lower than your friend's, it could make sense to sell yourself and give him the net after tax. A less appealing way to reduce taxes is to die- assuming your estate is less than the threshold (11.7 M in 2021 https://www.irs.gov/businesses/small-businesses-self-employed/estate-tax), then you could leave your BTC to your friend and they would get a basis that is stepped up to the value on the day of your death meaning they could sell without having to pay taxes (unless it appreciated between the time you died and the time they sold). When Yankee owner George Steinbrenner died in 2010, there was no tax on his $1 B+ estate AND his family got a stepped up basis meaning that nobody ever had to pay tax on the increased value of the Yankees and his other investments (at the Federal level). Had he died in 2009 or 2011, there could have been a $400 M+ tax bill.
Each state has its own tax laws so there may or may not be tax to be paid there also.
Its good that Trump simplified the tax system, otherwise it might not be so easy to understand Personally, I think we should do away with most income taxes and replace them with taxes on pollution and lies for profit.