Oh sorry, Helena, I didn't mean it to upset anyone - the gods know it's haunted me enough, since it happened. I'm trying not to think too hard about OP's neighbour's pup, must admit. I'd feel better if I could offer anyone else some pragmatic advice to help one other pup, somewhere. But all I could offer was 'Film it'. Which seems inadequate.
I would give anything to name and shame my neighbours - and take the consequences just to know that it was out there - and expose whoever it was sold them the new pup. My kids saw on FB - they have the pup as their banner and another pic or two up of it and it looks so incredibly sad, in every single shot that I keep wondering why no-one is challenging them or asking why it looks so traumatised. (I know it's not rescue as I heard her loudly opining outside that she wasn't having "any of that rescue shit" when she got a new dog).
My other neighbour was in the bath when it happened but he said if he'd seen it he would literally have gone round there and beat the shit out of them (and he would, too). It feels like we're waiting to capture something but of course that is like waiting for someone to hurt the poor pup. Yet the RSPCA told me that is any future pup's only hope.
At least pup in OP's case is outside and there is a chance someone down the street might be able to film it on their phone.
Think I'm ringing the council tomorrow to complain about the woman calling my son a "Nosy little shit" - but of course, the council won't do anythng even though it breaks their tenancy agreement (not to be abusive in the garden). She's seen my 14 year old trying to film her abusing the dog now, so will probably keep it even more indoors (it seems only to be allowed out briefly). Sorry for rambling.
I will always post on threads like this if I see them - just to out the RSPCA. (And the council, come to that, who could have banned them from having another dog after the first one died, given the concerns as recent tenants can only have pets with permission).