Chaz,
This post is not to be construed as legal advice.
See IRS Publication 969: https://www.irs.gov/pub/irs-pdf/p969.pdf which states:
Qualifying for an HSA
To be an eligible individual and qualify for an HSA, you must meet the following requirements.
You are covered under a high deductible health plan (HDHP), described later, on the first day of the month.
You have no other health coverage except what is permitted under Other health coverage, later.
You aren’t enrolled in Medicare. You can’t be claimed as a dependent on someone else's 2016 tax return.
My opinion (and it could be wrong) is that since the general purpose FSA has been exhausted and there are no more funds to be paid by the FSA. He & spouse are enrolling in the HDHP and they are no longer covered by her health plan or the FSA since funds are exhausted. Reading the above it appears that they would be considered eligible individuals. If the general FSA had not been exhausted then they would not have been eligible until funds were exhausted from the GP/FSA. You might want to read further in the publication to see if they are limited on the amount of deduction if they are enrolling in the middle of the plan year or less than full plan year. Just my two cents.