Councillor Stuart Littlewood has written to the council asking for an explanation of the payment the leaking of documents from 1992.
Mr Laverack was jailed last month for a number of offences committed in an earlier position with Cheshire CC social services, following an extensive police investigation.
He was arrested in 1995 while working for Cambridgeshire.
The next day Mr Unsworth appointed him manager of the Guardians Ad Litem Panel and confirmed by letter that he would still receive his financial settlement.
Mr Littlewood said: 'Mr Laverack hit the jackpot at tax payers' expense.
'The matter could easily have been kept above board by delaying his redundancy or bringing the new job forward.'
A council spokesman said the payment was acceptable because of the break in service.
He said: 'Mr Laverack's post of service development manager had disappeared as part of a downsizing exercise.
'He was therefore entitled to a redundancy payment.
'Mr Laverack subsequently had a break in service of almost two months before taking up the guardian ad litem post . . . to which he was well suited.'