I need assistance with gathering an opinion on a topic.
The ability from the Hexblade's ability Accursed Specter allows you to take the spirit from someone and create a specter. However an important part of it states.
"The specter remains in your service until the end of your next long rest, at which point it vanishes to the afterlife."

However the Specter's description has
"No such rest or redemption awaits a specter. It is doomed to the Material Plane, its only end the oblivion that comes with the destruction of its soul."

So I want to know if the afterlife involves the newly created specter's soul to be destroyed, The specter vanishes randomly to the material plane to await it's end, or if the soul passes on from the Specter to the other planes to meet it's proper afterlife bypassing the norm of Specters?

The bound soul raised by a Hexblade shares the stat block of a specter, but it has a different backstory/lore

I mean, the first sentence of the specter lore is

A specter is the angry, unfettered spirit

Obviously, the thing you raise using Accursed Specter is not unfettered since you're controlling it, so it's already different

A DM can certainly play it however they want, though. They could have all those specters gather in one place and eventually take their revenge on the warlock that's been dooming them to eternal torment rather than letting them pass on

This is a case of “Specific beats General.” The specific rules governing the Hexblade’s Accursed Specter override the general rules for the Specter monster.

Quote from Brian_Avery >>

What if you're multiclass and have access to Greater Restoration or have someone in the party who has access to that spell and they use it to counteract the effects of never taking a long rest.

If you never take another long rest, the specter remains in your service indefinitely?

 
The resources to cast Greater Restoration (100 gp worth of diamond dust & a 5th-level spell slot) far exceed the value of the Accursed Specter. Plus, the things only got 22 (5d8) HP + 3-10 Temp HP. They don’t last very long, and as undead they can’t be healed.

I feel like if this subclass feature had been made currently in D&D's lifespan, this "Accursed Specter" would have been given a unique stat block like the Steel Defender, Wildfire Spirt, Primal Companion, or the Tasha Summon spells instead of them finding a monster stat block that kind of fits what they want but now really. 

Does it gain the Specter's HP? Or only the Temp HP from the effect? My interpretation is that a creature must have HP to gain Temp HP, but I've been told I'm incorrect. If I am wrong, the Accursed Specter is stupidly squishy though.

It is a specter in every way, plus it gains the additional temp HP.

I think logically it would pass into the weapon that is your patron.