Help with accrual's between FY ends

Charity client with numerous funds & funders who operate from different and numerous bank accounts; on occasion they have two separate situations:

One fund bank account pays for expenses/salaries/TAX&Ni for another fund.  

One fund charges another fund for work carried out

This is typically dealt with by classifying the original payment as it's usage, and two cancelling contra entries are created to cancel out the original debt

However, in the situation where amounts are owed in the year prior, I've seen people in my practise classify the (debit) amount repaid as an accrual.

When this is entered into the bank account, the bank account will be debited and the accrual journal will be credited. Is this correct? I ask on the basis of being confused, I thought any credit increase to a liability account would ne contrary to what was attempting to be acehived i.e. clearing down accrual