Prompt acknowledgements of debt may be false (8)
I believe the answer is:
spurious
'be false' is the definition.
(I've seen this before)
'prompt acknowledgements of debt' is the wordplay.
'prompt' becomes 'spur' (I've seen this before).
'acknowledgements of debt' becomes 'ious' (I can't explain this - if you can you should give a lot more credence to this answer).
'spur'+'ious'='SPURIOUS'
'may' is the link.
Can you help me to learn more?
(Other definitions for spurious that I've seen before include "Plausible, but false" , "False, fake" , "Bogus" , "Not genuine or authentic" , "Forged" .)