Yes. The mother can claim them and get the refunds.
Don't worry about the pat 5 years, the IRS will make a decision on that and decide if hey will make those adjustments.
Since you spoke with the IRS and they have decided to not let you claim the dependents and all of the associated credits and you are sure that this is the result, you can prepare a return for you domestic partner. Be sure though because you do not want her to end up claiming the same children and your case is still pending. Let your 2021 case be finalized with the IRS first then file for her.
If the IRS decides to go back 3 years then you can file her returns at the same time. You just don't want to further complicate things.
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