unclear word order
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With this word order it is not clear here if the persons created the fields ("Felder") or the curators ("Kuratoren"). Other changes are great. More precise:
Bearbeiten von Feldern ist nur den Personen erlaubt, die sie erstellt haben, und den Kuratoren
Nur Kuratoren und Personen, die sie erstellt haben, dürfen Felder bearbeiten.
Still formally ambiguous but sematically obvious.
Your solution is shorter, but moves the subject and main verbs to the very end of the sentence. Semantically it says now clearly: Only curators and persons, which created them (=the curators), are allowed to edit fields.
What i don't understand: I made a suggestion and you have no point to criticise. But without hesitation you produce different a suggestion. Is there a deep doubt about me for some reason which allows to step easily over my reasoning?