Yes, he gets to deduct the $12k in year 3 and he has to include the $20,500 recapture as income or the return won't tie out to the basis for the calculation for recapture and it will look (to the IRS) like "he" underreported the correct amount of recapture; think about the overriding principle for a TP re: income/deductions...in general you can't take a deduction unless you realized income in some form. 

Since the recapture is income based off of an average of 2010/2011 alimony payments that $20,500 of income (the alimony recapture) would mean "he" took the $12,000 deduction in 2011.  If didn't report the $12,000 in alimony paid he would've had to recognize more alimony recapture because the average of 2010/2011 would be lower thus increasing the recapture.