Is a mentally incapacitated person (including an Alzheimer's patient) not required to pay the Ramadan fidyah, and is it permissible to give the Ramadan fidyah as a donation for building a mosque instead of giving it to the poor?

"A person who is insane is not obligated to fast or perform any other acts of worship, nor is expiation (fidyah (definition)) required on their behalf. If an Alzheimer's patient reaches the stage of complete insanity and total memory loss, they are not obligated to fast, make up missed fasts (qada'), or provide expiation (feeding). However, if they are in the early stages of the disease with partial memory loss but act rationally and recognize their family, they are considered obligated to fast as long as they are able. If fasting becomes an unbearable hardship and making up the fasts is also an unbearable hardship, then they transition to providing expiation (feeding). The expiation should be given to feed the poor, and it is not permissible to use it for building a mosque."