Is the money that the seller did not take due to a mistake, and then gifted to me in appreciation of my honesty, mine or my friend's, who asked me to buy the book?

The money is yours, not your friend's, because the seller gifted it to you due to your honesty and trustworthiness after the sale was completed. The reason for this is not the sale itself, but the gift given to the agent. Imam Ahmad said: "If a man gives another a garment to sell, and he sells it, and the buyer gifts him a handkerchief, then the handkerchief belongs to the owner of the garment." The author of Al-Mughni said: "This is because the gift of the handkerchief was caused by the sale, making the handkerchief an increase in the price." Al-Bahuti said: "If he (the seller) gifts him something after the two option periods, then it belongs to the one to whom it was gifted."