Your employer is not responsible to notify the HSA that you had left, although they probably should have stopped contributing to your HSA unless they confirmed that you were still under HDHP coverage. (maybe they did).
Probably in this case, she will have to deal with the excess. Yes, her annual HSA contribution limit will be limited to 5 months, assuming that she was under the new coverage on June 1st. (It's the first day of the month that determines the coverage for the month).
When she does the HSA interview in TurboTax and enters that she had only 5 months of HDHP coverage, TurboTax will tell her that she has excess contributions and ask her how much she will withdraw before the due date of the return.
If she is able to withdraw the entire excess amount (this is best), this amount will be sent to her as a check. TurboTax has already automatically added the excess to line 8 (Other Income) on Schedule 1 (1040), because this amount had been previously removed from Wages in box 1, 3 and 5 on her W-2.
Any excess not withdraw will carry over to 2021 and will be subject to a 6% penalty.
NOTE: she will need to contact her HSA custodian and ask for the "withdrawal of excess contributions with their earnings" (there is possibly a form on their website for this). She should do this by April 15th.
Last year, the IRS moved this date to June15th along with most other dates, but I have not seen if they have done the same this year for excess contribution withdrawals. NOTE, she does not have to have received the money by April 15th, just applied for it to be returned to her.
Does that cover everything?
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