ProjectionMatrix to camera attributes?

I am having a problem on an experiment involving Google maps WebglOverlayView and Three.js.

Basically I want that after an user interaction the scene, along with the 3d object and the camera, gets ‘moved’ on another canvas rendered by a new renderer.
The problem is that in the new state i’d need to be able to animate the camera attributes and the camera was handled by Google maps via only a projectionMatrix.

How could i ‘fill’ the camera properties (or clone it to a new one with the properties set) from its matrices?

My code is ATM heavily based on threejs-overlay-view/threejs-overlay-view.ts at 9de6c4ec096a6262f8a7965a814b3670600627a4 · ubilabs/threejs-overlay-view · GitHub

I tried several approaches to convert the matrices to the camera attributes to no avail:

Did setup a JSFiddle to explain better my question.
Clicking on the scene switches the cameras.