Moving to another state won’t impact your Social Security benefits, as these are federal, not state-based, so they stay the same wherever you live in the U.S. The only thing to remember is to update your address with the Social Security Administration so they have your current info.
If you're planning a big move, like to another state, it’s often worth getting help from a reliable long distance moving company to make the whole process smoother. It’s one less thing to worry about while you’re keeping track of things like address changes and settling in.