You correctly state that FHA loans carry a mandatory 5-year MI period regardless of LTV percentage, and after this 5-year period the your original LOAN AMOUNT must be paid down to 78% (not that the loan amount is 80% of current market value, which is typical for non-FHA MI removal). Hence, refinancing is the only way I am aware of to remove MI in your case. I am not aware of any FHA-to-conventional restriction.
This "78% or 5-year Rule" before Mortgage insurance can be terminated is covered here:
Also, any MI refund is based on a few things, and can be reviewed here:
Everytime you refinance, or establish a new loan, you are hit with all the closing costs. and the amortization table starts over again....I personally resist that option if the total objective is to remove the PMI. There might be another way besides refinancing...if they bring in 20% and get their LTV (loan to value) down under 80%.
As long as the borrower qualifies for a conventional loan and the property appraises, there shouldn't be any problems refinancing from an FHA to Conventional loan.
All the best,
Roswell Moore, CMPS
Certified Mortgage Planner