Have a problem with seemingly no solution:

Employee with HSA retired a year after being eligible for Medicare. Here are the dates:

12.2016 applied for SS & Medicare to start (both) 7.2017
6/30/17 last day of work
Medicare card says covered since 6.1.16 (which officially makes her ineligible for HSA contributions even though the correct date is 7.2017

Client makes several phone calls and nobody is willing or able to change the date on the card and reported to IRS. They explained to her that the date of application determines the date that the Medicare card shows and has nothing to do with the date actual coverage starts.

Having nothing in writing as to the actual date of coverage, how will my client proof to the IRS that they have wrong information. One would think that the IRS is aware of the issue (Medicare sure is but they say there is nothing they can do). Anyone else having this issue?