Timetracker - Invoice - Chart of accounts

Timetracker - Invoice - Chart of accounts

We have setup our "Items" to go to the correct chart of account. When we manually create an invoice, it goes into the correct chart of accounts.
 
We created the idential name as a "Task" under our project. When we convert entries from the time sheet to an invoice, we choose "Task" so that the "Task" name is where "Item" is on manually entered invoices. However, when we invoice this,  it does not put the timesheet "Task" entries into the correct chart of accounts, in fact I dont even know where it puts it.
 
We need to be able to have our employees enter time in the time sheet, create the invoice and have the "Task" time go into the correct chart of account. What do we need to do this? This will cause major problems with our accountant.