No. If your husband is a nonresident of the US and not a US Citizen and has abandoned his Green Card, then he does not have any obligation to file a US return IF he has NO US income. Having a SSN does not automatically mean you have to file a return.
If he does have US income and does NOT file a joint return with you, then he would need to file a 1040NR which TurboTax does not support, so he could use Sprintax.com or another company that handles the 1040NR.
As a nonresident alien, the tax laws apply differently to him. If he is not filing a joint return with you, then you would need to ask these questions to the experts at a company like Sprintax.com as they are well versed on the 1040NR.
Form 8833 has to do with Tax Treaty's. Tax treaties vary by country. If he is filing as a nonresident alien, this again would be a question for a 1040NR expert.
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