Issue:
Transferring Supplier Bills using Expense Code in Web Timesheet and Account/Item Numbers in QuickBooks.

Summary:
Supplier Bills can be transferred to QuickBooks if they are transferred using the Expense Type Names mapped to Account/Item in QuickBooks. However, if you map Web Timesheet Expense Codes to Account/Item Numbers in Quickbooks (instead of Account/Item Names) the transfer does not happen.

Explanation & Solution :
When transferring Supplier Bills you cannot map Expense Code to Account / Item numbers because the two values simply do not match. Whatever value you select to map to Account / Item, must match the Account/Item Name that exists in QuickBooks.
For example : If you select Expense Code (63530) and map it to Account Name (Mileage), you are trying to match:
63530 = Mileage
They do not match so no import can be performed. QuickBooks Integration Manager will throw an error saying "Account [63536] not present in QuickBooks"  QuickBooks Integration only matches on Account Name, never on Account Number. If you match Expense Type Name to Account / Item Name then the comparison becomes:
Mileage = Mileage
This a match is made and the import can continue.