Summary:
While trying to transfer time using QuickBooks Integration module for Billing purpose (Non-payroll timesheets), you may come across the following error QuickBooks did not process your request to save time entry for user [User_Name] while transferring time into QB.

Cause:
It is possible that, the option 'Use time data to create Paycheck' in QuickBooks is enabled for the employee for whom you're trying to transfer time. When you are transferring the 'Billing timesheet' using the Integration module having this above option enabled, QuickBooks will not know how to handle this situation. Hence, no time entries will be transferred from Web TimeSheet.

Resolution:
If you're transferring time for billing purpose, always make sure that ‘Use time data to create Paycheck' option is unchecked for users (Employees) in QuickBooks

Path: Employee Center-> Edit the Employee profile-> choose 'Payroll and Compensation tab' from the drop down. Uncheck 'Use time data to create Paycheck'.

If issue still persists, then try the below steps for the affected users.

In QuickBooks -> Employees tab -> 'Use Weekly TimeSheet' -> select those users whose time entries are not transferred -> It will display a pop-up window saying 'Would you like to use the time data for paycheck creation?' – click 'No'. Now, transfer the time entries.