The parol evidence rule is a rule of evidence applicable to the area of contract enforcement. What is the rule and how would it apply to the following?

Assume that James meets with Jasmine to discuss the purchase and sale of 4,000 units of microchips. They meet for a working lunch and go over things like but not limited to delivery, materials, cost just to name a few things.

They shake hands on the deal. James says that he better make some notes because, "My memory is not what it used to be". He jots down a few details, initials it and hands it to Jasmine.

Subsequently, James says there was never a deal. Can the writing be used as a sufficient memorandum of the deal? What if she signed it instead of James and James said it never happened... is there a difference? Please fully explain