If you relocate to another state and work 100% remotely, you can stop having New York state tax deducted from your pay and can stop filing a NY state tax return in the first full year that you no longer live in NY.
Since Florida has no income tax, you will save the amount that you normally pay to the state of NY.
If you keep your small business registered in NY after your move, you will need to continue filing in NY and also to register in Florida as an alien LLC. You may want to consider closing the NY LLC and starting a new LLC in Florida.
You should also consider the total costs of moving (which are not deductible except for active duty military service members), and the comparative cost of living in both locations.
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