Honestly, if you want a real deal Xbox One controller to work on PS4 (albeit wired through USB) then just buy a Brooks Super Convertor.
BROOK DESIGN LLC.
www.brookaccessory.com
The only drawback is it does have to be wired. But at least you can get the real thing running on a PS4 and its completely lag free. I have a few of these convertors. I have one for the PS4 to use my Xbox One Elite 2 controller with. I have one for the Dreamcast to use my PS4 controller with. I have one for the PS2 to use a PS4 controller with. I just bought another one to use with both Dreamcast and Saturn to plug in a wide array of controllers.
Since I have a PS4 Hori Arcade stick, these things have been a god send for me to use across platforms so my best recommendation really is the Brooks Super Convertors.
If you want the real deal and don't mind wired then the Brooks super convertor really is your best bet.
Otherwise look here for 3rd party alternatives that are wireless.
If you're a Playstation fan and envious of the Xbox One controller, these are some of the best recommended PS4/PS5 controller alternatives.
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