Padlock Alarm Help

[jkon]

I have a small padlock alarm that is powered by a 9 volt battery. I would like to power it with a 9 vdc wall wart adapter but would also want the battery backup just in case someone cuts the adapter power. I'd like to use a 9 volt rechargeable battery with the wall wart hooked up somehow to also provide a trickle charge to the battery. Is this easily possible without getting to elaborate because I have about twenty of these padlocks to do. Thanks

 

[chemelec]

This Circuit is Simple and should work fine.
I Show 10 mA, but you May want to even use a bit less.