This is one of those cases where care is needed. And it's not even one that came from the Guinness Book of Answers.
In fact I don't know where I first got this attribution, so I googled "william james scuba". This returned enough hits, including several from specialised diving websites, to reassure me that it's a reasonable answer: an Englishman named William H. James invented "the first practical scuba", the first "workable full–time" scuba, or "what is commonly agreed to be the first open–circuit scuba system", and he did so in 1825. (An open–circuit system is one where the gases that the diver exhales are released into the water, rather than being recycled and rebreathed.)
Wikipedia, however, doesn't mention William James on its Scuba diving page, and this particular William James doesn't have a page to himself either. According to Wikipedia, "The first commercially practical scuba rebreather was designed and built by the [English] diving engineer Henry Fleuss in 1878."
On its Timeline of diving technology page, Wikipedia credits Henry Fleuss with the development of "the first workable self–contained diving rig that used compressed oxygen." It describes Fleuss's device as a "prototype of closed–circuit scuba", which "used rope soaked in caustic potash to absorb carbon dioxide so the exhaled gas could be re–breathed." What William James invented, it says, was "a self–contained diving suit with compressed air stored in an iron container worn around the waist."
To summarise: I'd suggest that this is a complicated subject, which quizzers and question setters are advised to steer well clear of!
I was once asked "Who invented the original SCUBA breathing system?", and the answer required was Jacques Cousteau. This is a highly suspect assertion. Every serious quizzer should know that Jacques Cousteau invented what he called the Aqua–Lung, or aqualung – or at least was a key player in its development; but as the above discussion shows, this was not the first scuba.
The Cousteau Society explains that Cousteau's device "was inspired by the discoveries that preceded it, particularly that of Captain Yves Le Prieur, pioneer of autonomous diving who, in 1925, perfected an open–circuit, compressed–air device. There was one problem: the continuous flow of air limited how long the device could be used ... During the war ... [e]ngineer Emile Gagnan invented a demand regulator that would feed cooking gas to a car's carburetor in the exact amount the jet needed. Cousteau modified the regulator, adapted it and made it the crowning piece of his Self–Contained Underwater Breathing Apparatus (SCUBA), the Aqua–Lung."
Cousteau registered "Aqua–Lung" as a trademark.
© Haydn Thompson 2021