I would tell her right off the bat
"In order to conduct any business on this line,
-- I will need your full name and place of residence address with zipcode (No PO Boxes)
-- and your credit card number, name on the card, expiration date and security code
in order to go any further
Would you like to provide this info NOW for confirmation and a Purchase order to continue?"

Then just listen to the emptyness on the other end
If they continue tell them to call you back so you can retrieve any info they request then give them the number to your local police department.