There are a couple ways to do this.
The technical way to fix this is they purchase the home from you with FHA financing, or there is a slight chance it could be done as a refinance. FHA has a "kiddie condo" program where parents co-sign for their child as a non-occupant co-borrower, with the child occupying the home and the parents providing some/all of the qualifications. FHA also permits non-traditional credit, and actually just requires one of the borrowers to have traditional credit & credit scores, so other borrowers can have no credit scores, no traditional credit, and no non-tradional credit. With that done, you would fit Letter D on the list that cdtotten posted of being able to obtain another 2nd FHA mortgage.
It is a riskier transaction for a lender, because in the ultimate sense it is your rental property, and FHA loans are not to be used in that sense, however on the other hand your intentions sound earnest and you aren't looking to rip FHA off by abusing the program by accumulating rental properties via the non-occupant borrower feature, so it's a tough call to make. You would want to present this all upfront to the underwriter and let them make their decision.
If you wanted to avoid all of that then you could simply refinance your remaining loan amount into a non-owner occupied conventional loan, and then be able to purchase with FHA (those could be done simultaneously)... or you could do a non-owner occupied conventional cash out refinance on your current home, and then use it for the down payment on the new primary residence conventional and be able to avoid the monthly PMI if it's 20% or more.
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