- I always assumed the amulet came from W&H so that:
(a) they could have their apocalypse on their schedule, and not have some other evil git take over the world instead.
(b) they planned to entrap Angel within the amulet once he died so they could have him under their control afterwards.
Once Angel didn't use it, I suspect that W&H was done with it. They weren't interested in capturing Spike. They probably didn't think it was worth the trouble and likely suspected that Spike would cause friction with their target, Angel.
- I believe Lindsay found out about the amulet (or maybe he already knew it existed from his time at W&H since it is a very powerful artifact). He was delighted to create chaos.
Lindsay therefore extracted it and sent it to W&H knowing that whomever was within would be stuck there and that Spike and Angel pretty much hated each other. Perfect since he wanted to set the cat amongst the pigeons and revenge himself against both the Senior Partners AND Angel. Who better to accomplish that than the wild card vampire who fought for his soul & who wasn't supposed to happen? Extra points for the fact that Angel and Spike were in an adversarial relationship from the start of Spike's life. I don't think Lindsay really expected them to be allies even while really not liking each other. He doesn't really understand good guys. But Lindsay is nothing if not a trickster. If he can mess things up for the partners
and for Angel, he's a happy guy.
- The following is just my head canon, but....
I suspect the artifact itself isn't evil, just powerful and dangerous and reserved for an absolute "Hail Mary" situation to close an opening Hellmouth. I suspect it could never have been used by anyone unwilling to be a sacrifice - someone powerful and a champion (which is why the Senior Partners were certain Angel would use it). Maybe the trapping of the person making the sacrifice was a curse or perhaps it was a way for the forces of good to 'save' the essence of a champion who willingly sacrificed him/herself to save the world... Of course, once W&H got it in their custody, anyone who got 'saved' inside, was at their mercy. Power is always dangerous. Nothing is more dangerous than a powerful weapon in the wrong hands.