Airport Extreme

The AirPort Extreme cannot connect to the WiFi of a third party router. It can only connect to the WiFi provided by another Apple AirPort router.

To do what you want to do, you will need an AirPort Express. Apple discontinued this product in April 2018 but they may still be available as new, refurbished and used products on sites like Ebay.com

Otherwise, an extender sold by companies like Netgear might be able to do what you want as well.

Does your neighbor also have an Apple AirPort wireless router? Unlike the AirPort Express, you cannot use an AirPort Extreme or Time Capsule as a wireless Ethernet device for what you are trying to accomplish.