[NobodyReally]

I went from using XBMC Remote to using Kore for the remote on my phone and now the images will not save to my phone. When I open Kore and connect to Kodi, it will act like a first time connect and re-download all the images and information for TV Shows, Movies, etc.

Is there a setting in Kore that will let me save the image files to my phone? It's just annoying to let it load everything up for a few minutes when I connect.

(Space is not an issue, I have several gigs available).

[syncd]

No, the images aren't stored locally on your phone.
There's a cache that might serve some images locally, but it's a cache, so it's not guaranteed.