Is it true that the Prophet, peace and blessings be upon him, said: "He is not of us who shaves the mustache"?

We have not found what you asked about as a hadith. It is narrated in Sunan al-Tirmidhi and other collections that the Messenger of Allah, peace and blessings be upon him, said: "Whoever does not trim his mustache is not one of us," and Al-Albani graded it as authentic. It is also narrated in Sunan al-Nasa'i al-Kubra from Abu Hurayrah, from the Prophet, peace and blessings be upon him, who said: "The fitra (natural disposition) is five: circumcision, shaving the pubic hair, plucking the armpit hair, clipping the nails, and shaving the mustache." However, Al-Hafiz Ibn Hajar and Al-Albani weakened this narration with the wording "shaving the mustache."