Is it permissible to take the housing allowance designated for tenants, knowing that I live in an annex belonging to my father and do not have my own private accommodation?

You are not permitted to take a housing allowance if the decision stipulates that it is only for the tenant and you are living with your father for free. This is because a grant is subject to the condition of the grantor, and it is not permissible to resort to deception by providing a document that indicates tenancy when it is contrary to reality. This involves lying, cheating, and unlawfully consuming wealth. You may refer the matter to the responsible authority for their consideration.