I have been looking on line (including Partsconnexion) trying to find the value I need (400 v, 560 uf) with screw in terminals, but I cannot find anything matches.
400V is the minimum, higher voltage rating is better. Mouser has some 560uF 550V in stock.
Ambient temperature and internal heating due to ripple current is the most critical to the life of aluminum electrolytic capacitors. Although higher temperature rating is better, you also need to check the service life specification.
An aluminum electrolytic capacitor rated 85°C with service life of 18,000 hours can outlast one with 3,000 hours @ 105°C if working at ambient temperature lower than 85°C.
https://www.mouser.com/ProductDetail/KEMET/ALS60A561KE550?qs=nJQ%2FaDFn8AFl3GSdgkk75g%3D%3D