It may be easier for all if you have the b/f tape up the holes as he plans - would be difficult to mess that up - and as a safety measure buy your neighbour a carbon monoxide detector - but don't let the b/f fit it.
This will save...
Money for you - will not have to pay for fitting new flue
Trouble for your neighbour - will not have disturbance while new flue fitted
Your neighbours' lives - if the alarm goes off
Peccavi
March 2009