Is it permissible to gift perfume to a woman who will wear it out into the street, and is the giver sinful for that?

There is no harm in gifting perfume to a woman, as a gift brings affection and the giver is rewarded. If the woman uses the perfume in a forbidden manner, the sin is upon her. However, if the giver knows that the woman will use the perfume to go out to the market, it is not permissible for her to gift it, because that falls under cooperating in sin and aggression, in accordance with His (the Almighty's) saying: "And do not cooperate in sin and aggression."