It depends on when the current loan was closed and insured by FHA originally and whether it is a "streamline FHA" (refinance one FHA to another FHA loan at a lower rate). If it was before June 2009, the rules are different than after that date. But if I understand your question correctly, you are right that you effectively "keep" your current FHA insurance cost, not the new rates - as long as it is a streamline refinance.
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