usairways56

Everyone that I have heard from has said no, it's not possible, unfortunately. I recently built a new computer and my only choice was to clean install everything because my previous Windows was OEM. If you have a retail version of Windows you should be able to use the same license and not pay for Windows again, but the new hardware will most likely not work with the old OS SSD.
 
I'm betting you will have to clean install Windows. And once you do, you'll then have to reinstall FSX because Windows will not know that FSX is already installed, the previous registry entries will have been deleted. My recommendation and what I had to do is to:
 
1) Transfer all addon installation .exe's and 3rd party files from FSX drive (or wherever they're stored) to an external hard drive/thumb drive (don't forget to write down serial numbers) 
2) Clean install Windows on the OS drive. *have only the OS SSD plugged in to simplify things*
3) Make sure Windows was successfully installed. Log in, then plug in old non-OS hard drive and double check you have all the files you need before erasing it all
4) Format this non-OS drive as a new one
5) Reinstall FSX
6) Reinstall addons from the external hard drive/thumb drive
 
It would be a different story if you were just swapping non-OS hard drives, which can be done no problem, but a new mobo and old OS don't match. The upside to all of this is that you'll have a fresh machine with nothing to slow it down. It'll be a beast too. My rig is pretty similar to what yours will be and I pretty much ran into the same problem, I'm happy to answer any questions that I can about it

I have an i5 2500k OC'd to 4.2Ghz when I play FSX. I recently just upgraded to a GTX670 from a Radeon HD6770, but I'll reference to back when I had the 6770.
 
My FSX sliders are pretty much in the low/middle end. I put texture resolution up really high to look good, and autogen/scenery complexity about in the middle. Other than that, I don't find much else to be necessary for flying mostly IFR. (Feel free to chime in on that, I'm just going off the top of my head right now).
 
I'd get a pretty smooth 30 fps at FSDreamteam's Chicago O'Hare with the PMDG NGX and the Aerosoft AXE. I believe I would get around 25 fps at UK2000's Heathrow with the AXE. Up in the air would be about 60-80 fps depending on cloud distance and density, but my old gpu limited that and caused some minor stutters. 
 
*Note - I play on a lower resolution, I have an old monitor at 1024x768. Also, very low traffic, if any at all, because it kills fps so much.
 
In the end, I would say a 2500k and 560 can do the job, and I'd think they could get you that 20 fps. But you might be able to a bit better for around the same price with some good shopping. Lastly, once you upgrade to those parts and get a little better fps, you won't want to stop. All I ever wanted was a smooth 30 fps, and now that I have it, I want more.