You can only transfer between two firmwares in the 9.0-9.5 range, since the n3DS doesn't support emuNAND above 9.5.
However, if your NANDs are linked on the o3DS, you can transfer from sysNAND (since it's between 9.0-9.2 or can be updated to one of those versions) to either sysNAND or emuNAND on the n3DS.
Even if they're not, you can system format your emuNAND to unlink the NNID, then link it on sysNAND and proceed to use eShop spoof to system transfer, however this way you will lose your save data unless you back it up with SaveDataFiler first.
Oh I see, your o3DS isn't hacked. You're SOL in that case, unless you system transfer to a hacked o3DS on 10.1 emuNAND first. Then you'll be able to do what I wrote above.