Airport wlan and burglar alarm

Hey I have bought an ABUS burglar alarm. I thought its control panel was a wireless one. But it was only the contacts, PIR camera i.e that was wireless.

The controlpanel itselv must be connected to the internet via router. In my case a Netgear.

When my router and the control panel are placed far from each other, I have to draw a looong cabel. Not very easy. So I got the idea, that I could set up my old AirPort Express near the contolpanel of the burglarm alarm. Then connect it to my existing wireless network (from the Netgear) - and put a short ethernet cabel from the AirPort Express to the controlpanel of the burglar alarm.

I succeded to config. the Airport Express to my existing wireless network. The green light is on - but no connection between the control panel and the internet.

Am I complete wrong in my theory ... or? HELP please