Hi Stephen,
Copying blog post templates actually requires you to access your database and copy the template data from `#_easyblog_post_templates` and applying it in the database of the destination site.
May I know whether you want to keep your existing post templates table in your target site? If not, you can just export the post templates table and import it in your new site.
If you want to keep your existing post templates in your target site, then after exporting the table from your initial site, you can just edit the .sql file to exclude the templates that you do not want to copy.
As for your screenshot of the template, you can just copy the file over from your origin folder and put it in the folder of the target site. However, you have to specify the file path of the screenshot in the database of the target site after you copied the data over.
Reminders:
1. Keep in mind that you should backup your database beforehand in case anything unexpected happens.
2. Make sure the EasyBlog version between 2 sites is the same or there could be database conflicts.
3. After copying the post template data, you need to change the user id to correspond to any user id in your new site. So that there won't be any user error that appears.
Hope this helps. If you have any further questions let us know.