Nest Protect gen 2 battery to POE
You should find and measure the battery string voltage then jumper +,- to the ends. It is unlikely (yet possible) that middle battery connections are used.  They should not be jumpered.

If this assumption is untrue, then a virtual ground buffer must be added to split the supply to +/-4.5V such as possibly leaving the batteries in place with the 9.0V applied with a series R.

A DMM resistance check with each battery terminal to the PCB will tell you if the intermediate terminals are used.

Stack Jacks could combine 1 supply to all remotes if hardwired.