You would have to customize to achieve what you want. PARENT & WOCLASS are skipped in most cases and that causes the WO class to be set to WORKORDER & the task flag to be set to 0.
You could create an automation script called WORKORDER.DUPLICATE (and/or WOACTIVITY.DUPLICATE) to adjust the logic if you want to apply this consistently on duplication.
If you only want to do this some of the time, then you should create an automation script action that the user invokes to perform the logic.
Regardless on approach taken, during duplication you would set the parent to your WO (it's not valid to have a task without a parent), the WOCLASS to WOACTIVITY, and the istask flag to 1.
If you use the script .DUPLICATE event you'll have two implicit variables (dupmbo & mbo) for modifying and copying values. mbo is the original WO/task and dupmbo is the newly created record.
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Steven Shull
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