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) a gap or hole in a hedge, hence, wall, or the like, through which a wild animal is accustomed to pass; a muset. Muse(noun) one of the nine goddesses who presided over song and the different kinds of poetry, and also the arts and sciences; -- often used in the plural.