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Something to do with UV light and bacteria? Maybe. Science isn't my strong point. I once rescued a suitcase which had been doused with every known cleaning agent, but the cat stink never quite disappeared. I left it on the roof for a month. Now it can actually have human clothes put in it.
As an alternative to sunshine you can use UV bulbs. Which are also good for extending the life of a camera lens by killing any mould spores. (More of a problem with vintage lenses I think.) You can put a bulb inside a cardboard box so the UV light doesn't have undesirable effects. https://sensorex.com/blog/2020/01/22/does-uv-light-kill-mold/ I seem to remember that some people do this to sanitise pre-worn shoes....other people's fungus can be very persistent. The bloke who discovered Tutankhamun's tomb was killed by the Pharaoh's fungus.
Friends had a similar problem and consulted a cat psychologist. When two cats in one dwelling are enemies, the aggressor needs two or three litter trays. If there are cat flaps, each cat needs its own one. It's all about territory and smells. James wants dominance. He might compromise if he has more than Higgs, but he might not settle down until their zones are fully separated.
Sunshine eventually kills even the worst cat piss smell. If bleach and so on don't work, just leave the doormat outside for a few weeks.