Dear Fernando,
yes, you are right it would appear in not invoiced time and expense as time to be written off. Analogies for not making it clear in my last memo.
However with your query "We expected that if the task is marked as non-billable, in the time-sheet the hours would not appear as billable and additionally that time-sheet should not be taken into account for the "Not invoiced times and expenses". Is this correct?"
I think this is not possible as if you set at non-billable and at the time-sheet you set it as billable then this would appear in not invoiced time and expense with 'Quantity to be invoiced' and the same is followed to invoice request.
However if you set at non-billable and at the time-sheet you set it as non-billable then this would appear in not invoiced time and expense with 'Quantity to be written off' and the same is followed to invoice request.
In both cases be it bilable or non-billable it would appear in "Invoice Preparation: Not Invoiced Time and Expenses"
This is the current system behavior. Maybe an add-on or PDI to make it give error message when the time-sheet billable/ non-billable contradict the rule set as billable/non-billable in project.
However i will still try to check with SME about this architecture logic for you.
Regards
Leo