The most common and most likely answer to this crossword clue is the 9 letter word DELUSIONS
I've seen this crossword clue in The Daily Telegraph
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Buddy explains!

The straight part
We know that "False beliefs" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case false beliefs = delusions.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
Crossword Answer definitions
DELUSIONS noun- A false belief that is resistant to confrontation with actual facts.
- The state of being deluded or misled, or process of deluding somebody.
- That which is falsely or delusively believed or propagated; false belief; error in belief.