And here the description I lost on my first try:
The link in wgtest/index.html

Look <a href="http://www.Koizar.eu/wgtst/fürDich/test.html">here</a>!

should be converted to

Look <a href="fürDich/test.html">here</a>!

But it isn't. OTOH the backreference

Go <a href="http://www.Koizar.eu/wgtst/index.html">back</a>!

in wgtest/fürDich/test.html is successfully converted to

Go <a href="../index.html">back</a>!

I suspect the problem lies in or near convert_links_in_hashtable() in convert.c.

Here is a test case for those who want to investigate closer:

wget  --recursive --level=inf --convert-links  http://www.Koizar.eu/wgtst/index.html

In wgtst/index.html this line

+verbatim+
Look <a href="http://www.Koizar.eu/wgtst/fürDich/test.html">here</a>!

should be converted to

Look <a href="fürDich/test.html">here</a>!

but it isn't.  The backreference in wgtst/fürDich/test.html

Go <a href="http://www.Koizar.eu/wgtst/index.html">back</a>!

works:

Go <a href="../index.html">back</a>!

I suspect the problem lies in or near convert_links_in_hashtable() in convert.c.