You can consult this answer, but the instructions are a bit unclear, so I’ll clarify them myself here.
- On the old blog, export the posts using the standard WordPress import/export functionality. If you’re unfamiliar with that, see this link for more information: https://codex.wordpress.org/Importing_Content
- On the new blog, use the WP Importer to import the XML file generated when you exported the posts from the old blog, but do not click “Download and import file attachments”. You’ll be doing that in a later step. Import the posts.
- On the old blog download Export Featured Images. As of this writing the plugin DOES work with WP 5.1.1. I just tested it.
- Once the plugin is installed, go to Tools > Export Featured Images.
- Select “post” if you want blog images
- Click export. You’ll download another XML file
- On the new blog, visit the WP Importer once again.
- This time, click “Download and import file attachments”, then click “Submit”
This will assign all the featured images to the existing posts.
If you download and import file attachments in the first import, it will stop the second import from working.
Good luck!