The easiest method would be to simply swap the 06 covers/foam onto your 03 frames.
If swapping frames isn't an option...
Did your 03 have memory seats?
If yes, then you'll essentially need to pull the wiring/modules from your old seats, and install the in the new seats.
If no, the 06 seats should have the brown seat base connector still. Simply unplug the portion which routes to the DSM, and plug into your car's harness.
Then you'll need to cut and splice the recline, lumbar, airbag, seatbelt wires.
Or you might be able to simply swap harness.
Member of Northwest Panthers Car Club
2008 P71, Norsea Blue SAP
-Message Center cluster retrofit
-Towncar Signature L heated power seats
-Long overhead console
-Compustar remote start/security