Spirit Reaper needs to be designated as a target of an effect while face-up on the field and needs to be still face-up on the field at the end of the resulution, only in this case it is destroyed by its own effect.
Book of Moon targets him while it is face-up on the field, but it is face-down at the end of resolution, so it won't be destroyed.
Book of Life puts Spirit Reaper face-up on the field, but targets him into the graveyard, so it won't be destroyed.
Spirit Reaper will have to wait for Book of Moon's effect to resolve before it can destroy itself. But by that time it will already be face-down and it's text will be inactive.
EDIT: Ooops. Had an old window open and the baby was crying. Didn't see the many responces. My bad.
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