The concept Higher Self is syncretic term for what, on the LP we call Spiritual Ego.
Spiritual Ego > Atman, Augoeides, Buddha Nature, Genuine Self, Great Self, Higher Self, Highest Self, Holy Spirit, Immortal Spirit, Inner Self, Inner-Self, Monad, Monadic Intensification, Ohr, Original Face, Real Self, Resident Monadic Consciousness, Self, Soul, Spirit, Super Ego, Supreme Self, The Knower, The Witness, Transcendental Self, True Self, Universal Being, Universal Self
Sankaracharya, uses the term. "Let him by the Self, raise the Self."  That probably makes more sense formatted "Let him, by the Self, raise the self." This could perhaps be construed as a weak reference to Spontaneous Alignment.
- The Crest-Jewel of Wisdom and Other Writings of Sankaracharya. Translated by Charles Johnston. Kindle Edition. 1999: Theosophical University Press, 1946. https://www.theosociety.org/pasadena/crest/crest-1.htm.