The concept Higher Self is syncretic term for what, on the LP we call Spiritual Ego.
Spiritual Ego > Ajayu, Angel, Atman, Augoeides, Blazing Star, Brahman, Bright Light, Buddha Nature, Deep Self, Divine Ego, Father in Heaven, Genuine Self, God Self, Great Self, Guardian Angel, Higher Genius, Higher Self, Highest Self, Holy Spirit, Immortal Spirit, Inner Radar, Inner Self, Inner-Self, Intensification of Consciousness, Kra, La, Monad, Monadic Consciousness, Monadic Intensification, Neshamah, Ohr, Original Face, Paramatman, Real Ego, Real Self, Sakshi Chaitanya, Saug, Self, Soul, Spirit, Super Ego, Supreme Self, The Knower, The Witness, Transcendental Self, True Self, Unconsciousness, Universal Being, Universal Deity, Universal Self... further results
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.
Blavatsky describes the "higher self" as "the God within."
- 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.
- Blavatsky, H. P. The Key to Theosophy: A Clear Exposition Based on the Wisdom Religion of All Ages. Theosophical University Press, 1889.