In the your matter client father is depositer & Tax payer, so his mother can't sign on 15G or 15H
(If the depositor is not liable to pay income tax and the interest to be
paid/credited in a financial year does not exceed the maximum amount,
which is not chargeable to income tax, the depositor may submit a
declaration in Form No 15G so that income tax is not deducted at source.
Senior citizens (65 years and above) may submit a declaration in Form No
15H. Form 15G/15H should only be furnished by the depositors before the
prescribed date by the issuer.)