It is quite common for someone to mail a check at the very end of the year in order to include the amount in their expenses for the year. This does not necessarily mean that you received the income and have to include it on your income tax returns. They will almost certainly not be willing to change the 1099 to reflect this timing difference.
Additional information: Since your business is organized as a corporation, none of your clients needs to issue 1099s to you, although some will probably do so anyway.
If the total recipts you report for the year exceed the amount reported on all 1099s that you receive, you will not have any problems if you only include the income actually received from that customer. However, even if you need to report the full amount, there is a workaround. You will want to report the amount included on the 1099 but NOT received during 2016 as a miscellaneous expense. Use "1099 income not received" as the expense description.
Please note that whether you reduce your income or treat the difference as an expense, it will be 2017 income to you that will not be included in the 1099 that you receive from that customer.
