Sorry! I've just seen that it's an "old" Gigaset. It should still work, but I'm not entirely sure. Register a new handset on the old base station. Then send the numbers from the old handset to it. Put the new devices into operation, register them all on the new base station and then send the numbers again.
Sounds terribly complicated, but I can't explain it any better, or don't have a better solution :-(
It's quite simple: From the "executive phone" (which has the most and correct number entries) - open the phone book - Scroll down to "Send list" - "to internal" - all internal devices appear. Select device 1, ok and wait