With future perfect (F2) you jump to a point in the future, turn round and say some action is finished then. Actually a complicated thing and cumbersome and in most cases you can express the same idea much simpler without using F2. This tense existed in Latin and it was imitated by writers.
In current English usage, muse can refer in general to a person who inspires an artist, writer, or musician.
muse noun [ C/U ] (IMAGINARY FORCE) âº an imaginary force that gives you ideas and helps you to write, paint, or make music, or a physical representation of this force. (Definition of âmuseâ from the Cambridge Academic Content Dictionary Â© Cambridge University Press) Translations of âmuseâ.