You still have time to get a receipt/acknowlegement letter... As long as you have the receipt by filing time (April 18th this year, perhaps all the way to the last auto extension date - October), you can claim the deduction. There are some 'escape clauses' for donations of household goods when it's impossible for the charity to give you a receipt such as the Goodwill bin at the firehouse (or wherever), but claiming $15,000 this way would be suspicious at best.
Assuming you have a reasonably detailed list of what was donated, you probably can get your neighbor to take the list to the charity and get them to stamp it or whatever they do for donors and you should be set. Note that the charity will NOT value the items and it's now impossible to get a formal appraisal, which is required for 'donations of a group of similar items over $5000'. I'll leave it to you to figure out the grouping.
