Artem,
many thanks for your quick help!

I should have figured it out myself because of the meaning of "<image:loc>".

I am already adjusting the sitemap.
I will pass on your social media recommendation to the owner.
Just one more question:
The owner filled the description panel with informations and keywords, hoping Google would read them. I suggested to use tags, but he didn't like them.
Can Google read the description panel text if the pages are implemented correctly in the new sitemap?
Or are tags better for SEO?
UteS