Hi @mhutinet,
it seems these images were uploaded through a file field, but they are used inside the body field, so that’s why they have absolute paths…
I guess the only way to sort this out is maybe use a rewrite on the body field that uses some search/replace to adapt the URLs to your needs in the new site.
This module can help: https://www.drupal.org/project/views_regex_rewrite
Another possibility is to export the JSON as a file, then perform the search/replace offline, and use the result as input for the feed importer (I reckon you can upload a file directly instead of using a URL?).
Note: In any case, in terms of file management, you should really make sure that the files are imported through file fields, and not just directly copied on the filesystem, because this way you make sure Drupal will manage them and delete them or export them when nodes are deleted, exported, etc.
The part about getting a file field exposed by URL to be imported into a file field by a feed importer is covered in the post I wrote about exporting/importing content from D7 to D8: How To Export Content From D7 And Import It In D8 Using Views Data Export / Feeds Import
I just added an update today
Good luck!