Country A may be fine with you declaring you don't live in country A anymore. Depends on the country if they want to see proof you actually live in country B.
If they want to see prove, they may require a tax residency certificate, or simply a utility bill. It really depends on the country.
If country A doesn't want to see proof of new residency,︀ then just declaring this should be easy enough as far as country A is concerned.︁
As for country B, why would you have to tell them anything? Sure, you could︂ also officially move there and then tell them you changed your mind and moved back︃ to country A (or to country C), but then you'd be back to the question︄ above. I don't really see the point in this? If you're officially resident in country︅ B, then they'd probably ask for tax returns. And then you'd have to explain why︆ you're not paying any. So then you have even proof of tax fraud on paper.︇
In the end, it might work, but probably wouldn't, and if it did, the risk︈ of being charged with tax fraud would be very high.
If you want to commit︉ tax fraud, there are certainly less risky ways to do it (but please don't).
Not really, because they'd all︋ ask for your tax residency/utility bill etc., and there is still some remaining risk that︌ they'd report it to wherever you're really living.