Does anybody knows if a 25mm tire should be match to a 25mm rim? Total weight of Cap and Stoker is 290#.

If you mean that the outside width of the rim is 25mm then the inside width should be about 20mm. You'll be okay with 29-40mm tire according to Sheldon Brown. "If you use a very narrow tire on a wide rim, you risk pinch flats and rim damage from road hazards." I think you can do it, but it won't be ideal.
https://www.sheldonbrown.com/tire-sizing.html