According to sitemaps.org, all the URLs in a sitemap should be from the same host.
Also, all URLs in a Sitemap must be from a single host, such as
www.example.comor store.example.com.
source: https://www.sitemaps.org/protocol.html
Hence there is no question of including the canonical URL in the sitemap of the second domain. So you can only add the original URL https://second-url.example/text/my-post.
UPDATE:
Based on Stephen Ostermiller's answer (which should be the accepted answer), it is better to omit the URL in the sitemap of the second domain.