Yes. Each person included in the policy must file the 1095-A information on their return. Any listed covered person on the 1095-A, even if the main policy is in another person's name, you will need to enter the 1095-A on your return, unless you are claimed by a dependent on someone else's return.
You and your former spouse should agree on what percentage of those amounts you’ll claim on your return, and what percentage they will claim on their return. You can use anything from 0-100%, as long it all adds up to 100%.
Follow the steps in this link to enter your form. Where do I enter my 1095-A?
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