When and how to refinance out of an FHA

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Hello everyone!

I used an FHA to purchase a SFH that I house hacked in back in July 2020. But for career reasons I needed to move to a different city and am currently renting out the house. I have just a few questions,

when would be an appropriate time to refinance out of my current FHA mortgage?

how much would that cost and how long a process would that take?

would this impact my ability to house hack in my new city in any way?

Any feedback would be greatly appreciated!

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@Joshua Haynes they do have some flexibility if you need to move for family/career reasons