I would say that 'immortality' is not outside the scope of philosophy.
Think about the greeks, Pitagora taught and talked about past lives and he talked about himself that he had 9 past lives.
Platon, Aristotel, the Orphic poems, then Marcus Aurelius. Everyone in a different manner taught and talked about an existence beyound the physical one.
On the other hand philosophy is the "love of wisdom".
But this is an 'immortality' in a "religious" way, which way, i think, is not understood correctly, religions talk about us as spirits that come to this world in a body of flesh. See Hermes Trismegistus idea from Corpus Hermeticum, he says that when we die our body decompose itself in the primary elements and the soul goes back to his righteous place in "heavens". The idea is that we as souls/spirits (there is an amazing difference between these two, you can find it in alchemy, religion, occultism, etc) live in an "etheric" world and descend here - on earth - (see Plotin discourse/dialog 'about One and Unity' to understand the descending and ascending process) in a body to live as a human being.
So immortality as the eternal life of a soul is taught in philosophy or at least mentioned.
On the other hand, if you ask about the 'immortality' of our body from 'now' and about our 'now' self and thoughts, consciousness and all the characteristics that define us, i think it is the scope of philosophy too because 'immortality' may mean a healthy mind and body like in 'Mens sana in corpore sano'.
Anyway, 'immortality' is not outside the scope of philosophy because it fascinates us and philosophy is built on the things that fascinate us.