Answer
(Fatwa: 617/419/L=1431)
It is necessary for your farther to wash the part of the face in which he does not feel pain. Yes, the part of the face in which he feels unbearable pain and it is difficult to pour water or make masah, he can perform wudhu by leaving that particular part.
من به وجع رأس لا يستطيع معه مسحه محدثاً ولا غسله جنباً ففى الفيض عن غريب الرواية يتيمم افتی قارئ الهداية أنه يسقط عنه فرض مسحه (الدر المختار:1/433 باب التيمم).
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband