hi y’all.
There’s no built-in feature for setting a Featured Image on syndicated posts. This would require some custom PHP filters, or an add-on module, to provide it. As @crazylegsmurphy notes, there is a freely-available add-on that I wrote, FWP+: SIC ‘Em (for Syndicated Image Cacher), which attempts to provide some of this functionality. If you want to install this add-on and try it out, see https://github.com/radgeek/FWP—SIC–Em There are some underlying technical reasons, however, why SIC ‘Em can at best only make a guess at the right image to select for Featured Images, and cannot guarantee that the image it chooses is the same image that was used as the Featured Image on the source website.
The underlying issue here is that there is currently no widely-implemented standard way for RSS or Atom feeds to indicate the “Feature Image” to associate with a given post. If you look at the XML of the feed from a WordPress site that has Feature Images set on posts, there’s actually no tags that link to that image, unless it is also included elsewhere in the post content.
Now, the good news is that it IS possible for FWP+: SIC ‘Em to pick up more intelligently on this information, but ONLY IF you can install a plugin not only on the destination site (the site where you have FeedWordPress installed, and where the syndicated posts are supposed to be imported to), but ALSO have access to install plugins (or can persuade the site owner to install plugins) on the source site (the WordPress site that has the original posts you are trying to syndicate).
If that is the case in your situation, then you need (1) to install and configure FWP+: SIC ‘Em on the destination site alongside FeedWordPress; and also (2) get the FWP+: Pitch Media Gallery plugin at https://github.com/radgeek/FWPPitchMediaGallery and install and activate it on the source site that you are hoping to import posts from. If you are able to do (2), then the feed you are importing from will have new codes added to it, which clearly indicate to SIC ‘Em which image to import and mark as the Feature Image for each syndicated post that has a Feature Image assigned.
I realize this is a bit complex, but I hope it may either help you get what you need set up, or offer some explanation, with my regrets, of why it may be hard to get it set up under the circumstances.