You know, like how the Mouth of Sauron is just a mouthpiece and nothing more. Even his name was forgotten.
Many a time, I have see this type of exchange when dealing with a lore master character archetype, in a game style that places control over the facts of the world with the GM, and not with the players.
The GM describes something the players are not familiar with in the game world. For example, this can be a new Japanese corporation in Cyberpunk, a scroll written in a non-roman alphabet, or a reference to some as-yet unfamiliar past event. Let this be the mystery.
One of the character has a knowledge based skill that would fit perfectly to determine whether or not said characters knows something about the mystery established above. In fact, it is more than that: the player wanted to play a lore-master archetype, in other words someone who knows those things. Maybe they are gridlinked, maybe they have spend all their life inside a library, maybe they just read the right set of eldritch books. Whatever, the situation is that the character should know that information but the player does not.
Back to the mystery. Whether or not the dice roll to pass the skill test was successful or not†, the GM is left with either:
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Tell all the players a the same time, speaking in the voice of the character. Thus making the lore master character a glorified NPC a la Mouth Of Sauron.
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Take the lore master out of the room, tell them the information. Then correct things they have either missed, or misremembered, or got confused when they tell the rest of the players. This is tedious and takes way too much time.
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Be omniscient and have given said lore master player all the information they need at the start of the game/session. (Yeah, right.)
None of those solutions appeal to me for the reasons given.
† The way I handle the situation is that the player always gets some true information but the amount of false information increases based on the degree of failure of the roll. Never is there a point where no true information is ever passed. Edge cases are not covered here…
Best Answer
Let the loremaster improvise.
Start with the premise that "loremaster" doesn't mean "omniscience" or "retrocognition." There are many things that are not written down, not on the grid, were never recorded in lore, or have simply been forgotten or altered with time.
Make sure the player has a solid grasp of the themes of the game.
When it comes time for these rolls, should the rolls succeed, give them the crucial bit of information or clue that only you know. Then, ask the player, "So what else do you know about this subject?"
Let the player spin out the story of the corporation, the letter's sender, or the historical event, as per 2. Use those details to define and shape the campaign world.
If they get the tone completely wrong, or introduce elements you completely can't countenance, fall back on 1: The lore the player has spouted was once true but is now outdated, or was based on an erroneous translation, or was misinformation promoted by the enemies of the people under discussion. But for the most part, let the loremaster's lore be correct.
What you get from this is the chance for the loremaster to seem authoritative and the opportunity for you yourself to be surprised and inspired by his or her creations.