How can a husband legally prove his wife's ownership of one-third of the shared property, consisting of land and a house registered in his name, knowing that the wife contributed this amount, and they have four children, in order to clear his conscience?

Since you both have agreed that the wife should own one-third of the property commensurate with what she spent, this should be officially recorded and documented to safeguard rights. The title deed should be made joint between the husband and wife in this manner (two-thirds for the husband and one-third for the wife). It is permissible for a father to make his children partners with him in the ownership of a property to the extent of the money they contributed to its construction. If the wife participates in purchasing a property or paying its price, she has a share in it proportionate to what she paid, unless what she paid was a gift from her.