A dependent can't have an HSA account.
She can file her own return as a 'non-dependent' and indicate that she was 'covered all year' for Health Insurance. No details about the type of insurance or whose policy is needed, unless you shared a Marketplace plan reported on a 1095-A.
As long as she had an HDHP for the two months she made an HSA contribution, there will not be any issue.
If you claim her as your dependent, you will have excess an HSA contribution, which will be taxed and a penalty imposed if not removed.
Here's more info:
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