First, a disclaimer: this is not a conspiracy theory. What follows does not constitute evidence of a conspiracy. I am not a conspiracy theorist, in fact I loathe conspiracy theories. Don your tin foil hats and read on.
Dusko Popov was the star of a growing cadre of double agents being run by MI5. In 1941 MI5 had a problem: it controlled a network of double agents in Britain and had created a much larger network of fictional agents. Agents, even fictional agents, need money and the funds the Abwehr was providing was insufficient to support the double agents and fictional spies. Money was being brought in by German agents attempting to infiltrate into Britain and MI6 and MI5 was busy catching them and either turning them into double agents or imprisoning them if they refused to cooperate. There was always the risk that the Abwehr would guess that its infiltrated agents were in fact double agents and that their spy networks were entirely made up since spies do not usually work pro bono.
MI5 concocted a clever sting: they invented a fictional collaborator, a wealthy theater agent who was convinced that Britain would lose the war and was desperate to transfer his money out of Britain to the US but was unable to do so because of currency controls. The Abwehr would transfer money into the collaborator's account in the US and he would supposedly pay out an equivalent amount to designated German agents from his bank account in Britain. MI5 nominated Popov as the go-between between the theater agent and the Abwehr. It was a good deal for Popov: he got a 10% commission on transactions for his trouble and could finance his rather extravagant lifestyle. In reality the money sent to the account in the US went straight to MI5 and contributed to funding its operations.
To maintain the cover story, Popov had to travel between Britain and the US to arrange the fictional transfers. This suited the Abwehr just fine: Popov was asked to recruit a network of spies in the US.
On the eve of Popov's departure for New York in August 1941, the Abwehr sent him a long questionnaire for his spying. In the questionnaire was a section about Pearl Harbor; detailed questions about Pearl Harbor's defences, docks, ammunition and fuel dumps and significantly questions about the depth of water in the harbor, a critical detail if you were going to conduct an attack with torpedoes dropped from airplanes. Popov's Abwehr controller pressured him to make a personal visit to Pearl Harbor himself.
Once in the US, Popov and the resident SIS chief paid a visit to the FBI, meeting with the big guy himself: J. Edgar Hoover. Popov and the MI5 resident warned Hoover of the Abwehr's suspicious interest in Pearl Harbor and since Germany had no means to attack Pearl Harbor, clearly the information was meant for Japan, who definitely did have the means to attack Pearl Harbor.
The meeting didn't go well. J. Edgar Hoover and Popov did not hit it off and Hoover took great umbrage at Popov's suggestion that he look into Abwehr interest in Pearl Harbor.
It's easy to point to this curious incident and build a conspiracy theory on it. So what parts are true and what parts are suspect?
The Abwehr questionnaire about Pearl Harbor is in the public record and is certainly true.
Abwehr interest in Pearl Harbor and establishing a spy network in the US prior to its entry in World War II is well attested too.
The account of the tumultuous meeting between Hoover and Popov seems more dubious. The primary source is Popov himself, recounted in his autobiography in 1974. Me, I doubt that Hoover met with Popov; spies, and particularly double agents, tend to self-importance and narcissism and Popov had those traits. I just can't see Hoover meeting with Popov on at least a couple of occasions, it was bad tradecraft at a minimum and not in keeping with the care MI5 took with Popov and their double cross network.
So why was the Abwehr so interested in Pearl Harbor in July 1941?
That the Abwehr would gather pre-attack intelligence for Japan is unlikely considering the great pains the Imperial Japanese Navy took to keep the operation a secret (cf. ) The IJN had its own sources of intelligence, including an IJN officer working in the Honolulu consulate that kept a very close eye on Pearl Harbor.
Secondly, the timing does not really jibe with the timeline of Japanese preparations for the attack. The attack plans had already been worked out and tested in wargaming. Japanese aerial torpedoes adapted for shallow waters had already been developed and pilots were training in their use. The seemingly telling clue in the Abwehr questionnaire to an attack on Pearl Harbor - the question about depth of Pearl Harbor - was already known to the IJN.
Germany had its own reasons to want intelligence on the US Navy. It was in an undeclared war with the US in the Atlantic and how the USN disposed its forces between the Atlantic and the Pacific had a direct impact on German operations. So German interest in how the US Navy was forward deployed at Pearl Harbor was not out of place since it was directly related to how the USN struck that balance.
One last possibility is that the Abwehr wanted information on Pearl Harbor for an intelligence swap with Japan. Pearl Harbor was an obvious target for Japanese attack. Japan was much better placed to observe what the USSR was doing with its forces deployed in Siberia. Pearl Harbor intelligence for intel on Red Army deployments in Siberia would have been a good trade.