Transferring Single Transactions from a Unrestricted Fund to a Restricted Fund and then Move these Transactions to another Restricted Fund

You can use the Transfer funds feature, William Henry. This is the easiest way to transfer money. 

Although, you're unable to transfer the transaction itself. But, this lets you transfer money from Unrestricted Funds to the Restricted funds account. I'll guide you how:

1. Click the Banking menu.
2. Go to Transfer Funds.
3. Click the TRANSFER FUNDS FROM drop-down arrow, then select the Unrestricted funds account.
4. Click the TRANSFER FUNDS TO drop-down arrow, then select the Restricted funds account. 
5. Enter the amount in the TRANSFER AMOUNT field.
6. Add the date, then click Save & Close.

Once done, you can use the same steps above to transfer an amount from one restricted fund account to another. Then, just click the CLASS drop-down arrow to select a class. 

As always, I suggest conferring your tax adviser on the best way to handle this.

We're just right here if you have other technical questions about QuickBooks. 

Easiest way would be to find the transaction and then change it from one unrestricted to your correct restricted fund. If the cost is accross multiple funds then you can journal the costs by debiting the costs with the class of the restricted fund and credited the the costs to the unrestricted funds. It'll have no effect on the overall profit and loss account but will move it into the correct class for reporting. Alernative you could split the bill/payment on a class by class basis but this would mean the system would not automatically split the amounts the next time you receive a bill/make a payment.