It is proven that `Umar (radhiallahu anhu) had a long moustache and he used to twist it as well.
“ اذإ ناك هبراش لتف بضغ “
This is authentically narrated in Imaam Ahmad’s Kitaab ul-`Ilal wa Ma`rifatur Rijaal (2/73- 1589)30; Tabraani’s Mu`jam al-Kabeer
But at the same time it is proven that `Abdullah ibn `Umar used to trim his moustache so thin that his skin used to be seen as the prophet (peace and blessings be upon him) commanded to trim it Now the better stance is to not trim it completely or fully and using a razor or shaving the moustache completely is not proven from the Prophet, the Sahaaba, Taba`een but we can find this act among the Taba Taba`een such as Sufyaan ibn Uyaynah (rahimahullah) – an esteemed muhaddith of Makkah – but it is better to not shave it completely, rather trimming is better.
~Shaikh Al Mohaddis Hafiz Zubair Ali Zai Rahimahullah
