Oh dear, I'm sorry to hear what happened to Moe
If it helps, I don't know if anyone mentioned it but this happened to Chuggaconroy when he did his let's play, when Biskit moved out without his knowledge. It's an awful feeling to be in, but sadly as is the case of AC, animals come and go and if they want to go, they'll want to go. ;_;
Animals moving without my knowledge were more common-place in Wild World than New Leaf though, and I mentioned in a past thread that Tank ditched me on my own birthday. Other great villagers left me from that same town too - Baabara, Walker, Angus (though I didn't really care much for the Crankies then), etc etc.
Either way, the least I can do is offer the same advice as I do to anyone who's got an animal going - treasure the memories and move forward. Whoever takes Moe's place would be able to build new memories on top of pre-existing ones, whether you like them or not. And someday, when the 16-villager cycle boots him out, I say go look for him again and things will soon come full circle.
For now... virtual hugs from everyone :')