Are you
sure this is a Legit buyer? Unfortunately, the market is full of scammers who have no intention of actually buying your timeshare. A scammer will always insist on doing the closing themselves, or using their own company, and in most cases, they pocket the bogus closing costs, and ride off into the sunset.
Red flags:
-You got a cold call
-They are offering far more than the current market value
-There are fees they want you to pay to them or their agent
Whatever you do, don't send the buyer, or their agent any money for fees - all payments should go to the reputable closing company of your choice.
Tell the buyer that you will pay all the closing costs, and therefore you want to use your closing company - a scammer will make up all kinds of excuses why they can't do that.
I recommend that you contact a reputable closing company and let them handle everything for about $150. That is the best way to make sure it's done right, AND they can spot a scam, if it is a scam.
I use the following company - they are Tuggers, and they get high marks on TUG:
L.T. Transfers
Lisa Short and Mary Pless
http://www.lttransfers.com/
readylegal@gmail.com
706.219.2709