My husband received a 1099misc for $48,000 but he still hasn't received the last payment of $12,000; and it is past December 31, 2017. What year do we claim that income?

The standard is 'Constructive Receipt'

The income has been credited to the taxpayer's account or otherwise becomes available for him or her to draw upon in the future. Constructive receipt of income prevents taxpayers from deferring tax on income or compensation they have not yet utilized or spent. Reference: https://www.investopedia.com/terms/c/constructive-receipt.asp#ixzz535S7GQhS

From your description, you did not have constructive receipt and the income should go on next year’s return.  If you get the check tomorrow and it is dated December 2017 it is not 2017 income. Your problem, apparently, is that the payer wants to deduct it in 2017. So, he’s included it on the 2017 1099-Misc. So, he’s probably not going to want to issue a corrected 1099-misc.

 If you received an erroneous 1099-Misc, you have several choices (I would use #3):

1. Ideally, you get a corrected 1099-misc from the payer

2. Don't report it on your return. Attach a copy of the 1099 and a statement explaining the circumstances. You can't e-file. From the IRS instructions for form 1099-Misc: Form 1099-MISC incorrect? If this form is incorrect or has been issued in error, contact the payer. If you cannot get this form corrected, attach an explanation to your tax return and report your income correctly.

3. Report the Income on schedule C and take a deduction under other expenses, call it something like "constructive receipt adjustment"

4. Do report the extra $12,000, and hope you can explain it away when & if the IRS contacts you