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I think it all depends...
Personally I collected from the state of Florida.
I moved to Indiana.
I went to Fl unemployment before moving and expained I intended to move out of state.
Search for a job would of course continue but not in Fl.
They told me to let them know the date I intended to leave...arranged with me to mail my checks to the address I intended to go to in Indiana for a specififed amount of time.
Before the end of the specified time I had to "check in" at Indiana Unemployment.
Indiana Unemployment made an arrangement with Florida Unemployment (I do not remember specifics, but it all went very smoothly)
BUT, though paperwork changed, and I began reporting to Indiana my checks remained the exact same and I beleive, if I recall correctly, they were still mailed to me from Florida.
So I suggest you contact your local unemployment office and find out how it works in the state you are leaving and the state you are going to.
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