Can a Hexblade warlock use their Accursed Specter feature as a pseudo-Speak with Dead spell?

Question

The enemy criminal is captured by the player, and a middle-ranking one of an enormous organization at that. There's no way he didn't know the high-rankings, otherwise he couldn't coordinate with the lower ones. As a middle-rank, he must also know the mundane, day-to-day stuff or he wouldn't be able to organize his Crime Cell.

By my—the DM's—roleplaying, he is not someone that would easily leak information. As a field leader of his smaller Crime Cell, he had the experience of being dead at least three times and are trained in anti-torture training. He constantly talks back, goad the PCs to emotional, not caring if he's going to be killed or not, because at some point the organization will sent an evil cleric to revive him in the future, like in the past. (The players killed him before I managed to hint why he had this uncaring attitude.)

Anyways, the players giving up on interrogating. The Hexblade warlock PC decapitates him, and raises his soul as per Accursed Specter:

Starting at 6th level, you can curse the soul of a person you slay, temporarily binding it in your service. When you slay a humanoid, you can cause its spirit to rise from its corpse as a specter. When the specter appears, it gains temporary hit points equal to half your warlock level. Roll initiative for the specter, which has its own turns. It obeys your verbal commands, and it gains a special bonus to its attack rolls equal to your Charisma modifier (minimum of +0). The specter remains in your service until the end of your next long rest, at which point it vanishes to the afterlife.

The Hexblade then asks the specter if he can understand her. As per Specter's monster stats, Specter do understand the language, just can't speak. The Hexblade then orders the Specter to answer her questions with "Yes" by nodding, and "No" by shaking its head.

Because of "The Specter remains in your service until the end of your next long rest", that means the Specter can be continually asked for a long time. Meaning there would be a lot of fundamental things that they can ask, if they had the right idea. Also, it had advantage over Speak with Dead because they are compelled to 'answer' truthfully when ordered.

Now, for this particular enemy I'm not too worried because his area of influence are only the capital where the PCs have transit, and orders are sent through Sending. But what about in the future where they managed to snag a high rank? The Organization is thousand-year old criminal group, and they even had a rulebook for their regular guards about To-do and Not-to-do that are based on their own ingenuity of slipping through guards, dozens of evil cleric capable of revival, etc etc. This Accursed Specter seem to be a kind of weak spot they wouldn't normally left open.

Should this be allowed?

(I already okayed it by "That is an excellent creativity. For this time, alright. It's both as-written and doesn't fully overlap with Speak with Dead. But I'll ask around later in case you want to do it again. There might be some rule or something I didn't remember prohibiting this")

Answer 1

Per rules as written, the specter knows nothing of their previous life.

The relevant part of the description of the Accursed Specter feature tells us that:

When you slay a humanoid, you can cause its spirit to rise from its corpse as a specter, the statistics for which are in the Monster Manual.

If one looks at the Specter entry in the MM, one can find (emphasis mine):

Specters no longer possess connections to who or what they were, yet are condemned to walk the world forever. Some are spawned when dark magic or the touch of a wraith rips a soul from a living body.

Since the description is part of the monster statistics, the bolded part says that actually the specter does not have any connection to their previous life, hence a strict reading states that he cannot answer to questions related to their crime activity.

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As DM, you can overrule this.

Per rule 0, a DM can decide otherwise and let the specter be able to remember particulars from their previous life, and even to behave as they were in life. I am referring to this enemy who:

talks back, goad the PCs to emotional, not caring if he's going to be killed or not, because at some point the organization will sent an evil cleric to revive him in the future, like in the past.

Answer 2

It doesn't matter -- any clandestine organization in a magic world, has to be built to withstand magic

If it's not Accursed Specter or speak with dead, it will be charm person, detect thoughts, dominate person, or something else.

More mundanely, while there is ample evidence that interrogational torture is ineffective, plain old espionage and investigation make it hard to keep secrets secret.

And, in fact, one of the best tactics is just to offer a member of the Organization a better deal. Almost anyone can be turned, with the right leverage.

Use obfuscation and misdirection

You alluded to a clandestine cell system. You're on the right track. Any thousand-year-old clandestine organization would have to have layers upon layers of indirection and obfuscation.

Fight magic with magic

Any thousand-year-old clandestine organization in a magic world may well have developed magic to deal with just this situation. Members might be enchanted to have false memories, or obscured ones, or their minds may be shielded in some way.

Even within a cell, an operative may just know their colleagues by not just pseudonyms, but maybe by identities completely obscured by magic. If five members meet, and every one is disguised in some specific way, for instance, as animal-people, at most one member can say that they meet with a cat, a dog, a fox, and a lion.

If your captured operative can only ever say, "I get my orders from the cat", they might not be giving up much.

An old fantasy novel, A Shadow of All Night Falling (and its sequels) illustrates this beautifully. Within the Dread Empire, there is a conspiracy whose warrior-wizard members only ever meet wearing armor and masks, and often meet in magically obscured locations. They may well deal with a cell member day-to-day and not know it.

If your organization has lasted a thousand years, its built to withstand minor compromise, or even to shed whole sections of itself. Some group of meddling PCs is going to have to do more than compromise one or two members to make any significant dent in it.