I'm looking for a device like a cordless doorbell but with an infrared
detector rather than a push-button.

It's to mount in a shop near the door so that when someone comes in it
alerts the person in the back room that someone has come in.

It needs it to be cordless rather than having to be wired in.

(This is for use when the door of the shop is left open in the summer -
there is CCTV but that wouldn't stop someone nipping and running off
with something if the owner wasn't looking at the monitor all the time)

Can anyone suggest any websites that sell such things?

Thanks