Is the husband obligated to pay rent for the years he lived in his mother's apartment to achieve fairness between him and his siblings, knowing that his mother paid the full price of the apartment and registered it in her name?

If a mother houses her son in her apartment in exchange for a known rent, then the son must pay it. However, if the housing is in the form of a loan ( 'ariya ), then the mother has no right to demand rent. Housing the son as a loan is not considered preferential treatment that necessitates compensation for the siblings, as long as it is to fulfill his need for housing.