I unsderstand that i am just a forum member but i felt the need to let those who dont know.
Spirit Reaper's effect is as follows:
''This card cannot be destroyed by battle. Destroy this card when it is targeted by a Spell, Trap, Spell/Trap effect, or Effect Monster effect. When this card inflicts Battle Damage to your opponent by a direct attack, your opponent randomly discards 1 card.''
If you book of moon a spirit reaper, reaper is not destroyed as spirit reaper would be destroyed at resolution but before resolution it is flip face-down therefore spirit reaper is no longer face-up and not destroyed.
Spirit Reaper's effect is as follows:
''This card cannot be destroyed by battle. Destroy this card when it is targeted by a Spell, Trap, Spell/Trap effect, or Effect Monster effect. When this card inflicts Battle Damage to your opponent by a direct attack, your opponent randomly discards 1 card.''
If you book of moon a spirit reaper, reaper is not destroyed as spirit reaper would be destroyed at resolution but before resolution it is flip face-down therefore spirit reaper is no longer face-up and not destroyed.