Two ways to do it.
A )
Connect the gas posts and have it a closed system... in which case you would be filtering by gravity.
So - kegs at the same pressure - connect liquid posts via the filter - connect gas posts directly - full keg up on the bench and empty keg on the floor. A quick pull on the gas post of the bottom keg to get the flow started and the rest happens by syphon/gravity. If it slows down, just release a little more gas from the bottom keg.
B )
Do it like you were counter pressure filling the empty keg from the full one.
Gas regulator connected to both kegs at the same pressure - make it a higher pressure than the carbonation pressure, this will stop any gas coming out of solution during the process - liquid to liquid posts connected to each other with the filter in between. Now - nothing is going anywhere right? OK take the gas off the empty keg (still nothing going anywhere) - and let a little pressure out of the empty keg... but don't just lift the pressure relief and leave it up. Bleed it out slowly so the total pressure in the system never drops below the carbonation pressure and the liquid flows nice and slowly. This way you control foaming and you don't lose any carbonation - it also avoids too big a pressure differential across the filter, which can force yeast through and permanently damage the effectiveness of the filter.
Filtering carbonated beer is a pain in the bum - but it is manageable if you are careful.
TB