Question:

What is the ruling of the hair that grows below the lips and above the beard? Are you allowed to cut it? What is the ruling of the hair that is at the back of a thick beard by the neck?

Answer: حامدا ومصليا ومسلما

The jurists have stated that, to shave the mouche or its surrounding area i.e. the hair below the lips is an innovation (bidah).

(Behishti Zewar 11/774)

It is best not to shave the hair on the neck. However it is narrated from Imam Abu Yusuf that he said there is no problem in such. (ibid)

It is permissible to pluck and shave the hair of the neck. However it is best not to shave it.
(Fatawa Mahmoodiyyah 8/282)
And Allah Ta’alaa knows best.
(Hazrat Mufti) Ahmed Khanpuri (May Allah preserve him)
(Mahmoodul Fataawaa 4/723-724)