(I kinda listed them in the order of their speed, but 1. is useless on its' own if you want a subrect, since there is no SFML pure way to get a subrect of Texture into new one, I don't know if there is a GL way to do that even, but there might be. If you do it only on 'unit save' then speed shouldn't matter anyway so I'd say go for 3.)
1. Texture has update method that you can use to download entire window into it (but you probably want a subrect...).
2. You can use RenderTexture for the image editing space itself and copy its' internal texture when you are done and then throw away the RenderTexture itself.
3. RenderWindow has capture method which will get the window's content as an Image and then you can load (a part of) that to Texture using loadFromImage with custom subrect.
1. is pure GPU (but useless if you want a subrect), 2. and 3. take a trip through CPU.