Because we are now in FY20 and the bilateral modification deobligating FY19 funds was, in fact, signed by the contractor and signed by the CO (myself), what is the best Claim process given that the "work was performed" however it was never invoiced as requested and instead signed that he agreed to deobligate the funds due to his not invoicing? Specifically, does the CO stand by the mod's determination and refer the contractor to the Small Business Board of Appeals or instead does the CO resolve within the Agency by requesting new FY20 funds to pay for the actual work performed and late invoice received?
Sometimes scenarios like this happen. I will make the assumption that it was an honest mistake by the contractor and they would not have agreed to the modification deobligating funds if they knew/realized they hadn't been paid yet. I will also make the assumption that the contractor completed the work successfully and it was accepted by the government.
My advice is to pay the invoice; see FAR 1.602-2(b). If my assumptions above are accurate, it is quite dubious the government would prevail should the contractor choose to file a claim. Furthermore, a claim under the disputes act would require a contracting officers final decision. Most agencies require the contracting officer's final decision to be reviewed by legal... I seriously doubt (again if my assumptions are accurate) any contract attorney would approve of such a contracting officer's final decision denying payment in this case.
Because of the Time Statute 31 U.S.C. § 1502 you will need to use FY19 funds. Your finance office should know the procedures and forms you will need to follow/fill out to request an Obligation Adjustment Requirement. There is a very, very good chance your agency still has FY19 funds. While these can't be used for new requirements (they don't expire for another 4 years) they can be used for adjustments on work during FY19, specifically for the purposes that your scenario represents.