Final answer:
The woman may prevail due to the necessity of using the woodworking tools in exchange for heating oil, assuming there was implied consent or privilege due to necessity, as the man had left without arrangements for necessary utilities.
Step-by-step explanation:
If the woman prevails in the lawsuit for conversion, the most likely reason would be that she had a necessity to use the man's woodworking tools to provide for her basic need of heating during the winter. Conversion is the unauthorized act of depriving an owner of personal property without their consent. However, in this case, the woman might argue that she had an implied consent or a privilege due to necessity to use the tools in exchange for the essential heating oil, especially considering that the man abandoned the residence without providing for the continuation of necessary utilities.