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Medicare Answers
I have not seen evidence of a possible change in Social Security disability payments when moving to another state. I am almost certain retirement benefits are a function of your work and earnings history -- not where you live.
It is, however, possible, benefits from state agencies may vary from state to state. Check the relevant state agency for details.
Here are some resources regarding moving that may be useful :
http://www.ssa.gov/pubs/10153.html#4
https://secure.ssa.gov/apps6z/ICOA/coa001.jsp