I just tried using the file which Vladimir attached in his last post and the string “Read more” got translated.
Go to “WPML -> String translation”, click on “Save options and rescan settings” at the very bottom in case you didn’t do this before.
Once the strings get rescanned, find the string named “[pi_theme_options]blog_readmore_text” and click on the translate link. Once you translate the string, mark “Translation is complete” and click on save button. Your string “Read more” should be now translated.
Check out the screenshot I provided.