Project Timesheet - Invoice - Chart of accounts

Project Timesheet - Invoice - Chart of accounts

We have set up our Items so they go into the correct chart of accounts. When we manually create invoice and choose the correct item, it goes into the correct chart of account. We have our "Items" linked to the correct chart of account.
 
We created the same (idential) "Tasks" under projects so when we create an invoice from our project time, the "Task" name will match the "Item" name. Once the project is invoiced, it is not going into the correct chart of accounts, infact, I'm not even sure what chart of accounts it goes in to, if any.
 
What do we need to do so our employees will enter time under Timesheet with the "Tasks" we provide, invoice and have the time go into the correct chart of accounts? This could cause some major potential issues with our accountant.