It does work from Moodle to Moodle. The problem seems to be that these xml cartridges (is that the right name?) are not supported by every LTI consumer, in my case this test website and Ilias, but Moodle requires them (at least for LTI version 1, which is the only option in my case). Found this here:
LTI and Moodle
LTI launch ever only shows .xml file
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