Salam 'alaykum... Is there any narration which says that after the death, nose of a true believer tilts to some degree?
All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
We have not come across a Hadeeth with the meaning that you have mentioned in the question. However, tilting the nose is a mark to make known the death of a person. The jurists have stated this in their literature. But this has nothing to do with having true belief or not having it. In Fatwa 206227 we have clarified some signs by which death is known.
Also, for more benefit about some of the signs of good endings to life, please refer to Fataawa 165983 and 101417.
Allaah Knows best.
You can search for fatwa through many choices