Would the Hajj be valid if the obligatory blood sacrifice for a shortcoming in the Hajj was paid for by the husband of the pilgrim's mother, knowing that the pilgrim possessed sufficient funds to pay for the sacrifice?

If someone neglects an obligation during Hajj or commits certain prohibited acts, a dam (sacrifice) becomes incumbent upon them. If a dam becomes incumbent upon that person, it is not necessarily required to be from their own money. Another person may donate it to them, or shed the blood on their behalf with their permission, with the importance of the person's intention when authorizing the sacrifice. However, if the sacrificial animal is slaughtered on their behalf without their knowledge, it is not sufficient, because intention is a condition for acts of worship.