the game on the controller of PS 4 (Assassin's Creed: Syndicate)

HELL DOG
Install DS4Windows.

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There he "likes" only gamepads designated as from Xbox, so yes, install DS4Windows or a similar program

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Or buy an official bluetooth adapter to dualshock 4.
Or play through a usb connection.
Or try to set up the controller through steam overlay. Even if the game is not in the steam, its label can be added as a side game and set up control.