I consider the term "false-belief" a bit tricky. "Belief" implies that the object of it is not certain. When someone is sure about something, this person would say "I know X" instead of "I believe X".
If I say "I know X exists", I have no doubt about it. If I say "I believe X exists", I'm considering that I may be wrong.
Nothing guarantees that the person who says "I know X..." is correct, this person may be mistaken, then you could say "This person believes X...".
Possibly by "false-belief" you meant "unaware of mistake", but anyway I thought this might add to the discussion.
If a person A states "This is X" ("I know X"), it is considered a knowledge, and as such, not an object of doubt. Some person B may find that A is mistaken and say "'A' believes this is X, but it is actually Y" ("I know 'A' is mistaken"). A 'false-belief' verb would only dislocate the source of knowledge/doubt, as there is no end to this. Some person C could say "'B' considers 'A' to be mistaken, but 'B' is wrong", etc. (As far as I'm concerned, all languages have such words as "mistake", "error", "fault", "confusion", "minsunderstanding" ... in some cases the noun maybe become a verb, as in "He mistook my intentions"; the mandarin case would only be some specific form of this)