Yes, you just program the cat flap to recognise the cat's existing microchip.
These instructions are from the Cat Mate flap, but I imagine they are all similar:
3. Programming
Program your cat’s microchip or I.D. Disc(s) as follows:
3.1 Press and hold the 'PROGRAM' button (H, Fig. 1) for 5 seconds until
the LED (A) illuminates. Wait a minimum of 10 seconds.
3.2 Encourage your cat to slowly pass through the tunnel by
holding the flap open as shown in Fig. 5 after checking the rotary 4 way
lock (E) is set to 'IN & OUT'.
3.3 When programmed, the LED will flash.
3.4 Press the 'PROGRAM' button to save the setting