Can a battery ring doorbell communicate with a hard-wired ring doorbell to use my in-home chime???

I have a hard-wired ring doorbell that uses my existing in-home chime and it works perfect. However, I also have an entry-way before my front-door that is usually unlocked; mostly for convenience & so packages can be left in the entry-way out of sight and protected from the elements. I want to put a battery chime on the entryway screen door (there is no power source nearby), and deactivate the camera (to extend battery life and since I already have a dedicated outdoor camera) *but* I would love for that doorbell to ring my in-home chime just like the hard-wired one does. Basically I want to see if the battery ring when pressed can somehow speak to the hard-wired ring & trigger the in-home chime. Is this possible somehow??? [I made a simple layout below. The blue door has the hard-wired doorbell that rings my house chime. I would like to put another ring (battery powered) on the green door to the entryway that can trigger the in-home chime via the hard-wired ring)