In case the first wife buys the sacrificial lamb with her own money due to her husband's absence and his marriage to another without spending on her, what should be said or intended when slaughtering?

A woman’s sacrifice is sufficient if her husband includes her in it, and a person may offer one sheep as a sacrifice on behalf of himself and his household, regardless of the number of wives, as they are all considered part of his family. If a woman wishes to offer a sacrifice from her own money, it is a virtuous act. When slaughtering, if the person performing the sacrifice is skilled in proper slaughtering, he should do it himself and say, "In the name of Allah, Allah is the Greatest. O Allah, this is on behalf of [name]," intending it for himself and his dependents. If he is not proficient, he should delegate someone else to do it, and it is recommended that he witness the slaughter.