Transfer of property through gift deed or will

Respected sir/madam, My father owned a house Which was a self acquired one.Due to old age he gifted The house to my mother through gift deed,when he was alive.After my Fathers death,my mother sold this property , which was . gifted by my father.After a year ,she purchased a site and constructed house from The money she received by selling the gifted house from My father.My query is ,is this House constructed by my mother becomes a self acquired one.i.e a self owned Property.Can she make a will to or a gift deed to any one as per her wishes.Kindly clear My doubts.Iam a Hindu.please do not publish my name and address. Thanks Umesh .