Can wAP R AC be powered by POE and DC jack simultaneously.

Hi, usually wAP R AC is powered by POE, but in case of power outage, I want to connect it to 12V batery. Should I disconnect it from POE - in case the power is restored - because, when power is restored it will be connected to both batery and POE, until I disconnect the batery.
If it can be connected to both, do you know, if there is a priority? For example, maybe it would take power by default from POE, and I could keep it connected to 12V batery for case of power outage.

You can use both power inputs at the same time.
From cold boot priority will be the one with higher voltage. In case you have lost electricity (power outage etc.), further it will be powered with next available power input.

Just use supplied power adapter (24V) to power device via PoE and you’ll be fine.

Just a tiny advice: use under-voltage protection relay to disconnect load from battery … not to drain battery to the level where it gets damaged.