You are correct he can claim NC as his resident state under the MSRRA. He would be considered a resident for the full year. His income from both WY and Japan would be considered NC income and taxable there. You would file an joint resident NC return.
In the "My Info" section both you and your spouse would select that on 31 Dec 2020 your resident state was NC. You would indicate that you did not live in another state.
Since WY does not have a state income tax and of course Japan is not a state, you would indicate that you did not earn income in any other state. This will preclude any non-resident returns from generating.
For future reference if you take action to establish residence in another state like WY or TX for example where there is no state income tax then you both would be claiming residence in states with no income tax no matter where you are stationed.
Perhaps WY is your residence state now??
You should seek the assistance of base legal/finance office to establish a new residency. NC says, "An individual who enters military service while a resident of North Carolina is presumed to be a resident of this State for income tax purposes. Residency in this State is not abandoned until a definite residence is established elsewhere. To change residency, the servicemember must not only be present in the new location with the intention of making the new location the servicemember’s domicile, but must factually establish that the servicemember has done so."
Here is a list of items to factually establish a change.
1. Selling a house and buying a new one.
2. Directing U.S. Postal Service to forward mail to a new address.
3. Transferring family medical records to a new health care provider.
4. Notifying senders of statements, bills, subscriptions, and similar items of new address.
5. Registering a vehicle in a new jurisdiction.
6. Transferring memberships for church, health club, lodge, or similar activity.
7. Applying for professional certifications in a jurisdiction.
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