B777 Captain reported a passenger attempted to board wheelchair labeled as 'Airline Approved' by vendor. After further research; it was determined the airline's additional restrictions required the battery to be removed and transported in the cabin prior to departure.

Narrative

I was Captain of Air Carrier X [Flight] XXXX from ZZZ to ZZZ1. During pre-flight; I was notified there was an incident with a Dangerous Goods. A passenger had a collapsible motor cart for moving through the airport and wanted to check it into the cargo pit while traveling on our flight. The ramp agents; following Air Carrier X procedure; tried to identify the battery type on the cart. The cart had no identifying markings or easy accessible battery to inspect. I was called to make a decision.I looked at the cart and agreed it wasn't identifiable. We asked the owner who said she had no documentation; but had bought the cart at Store X. She stated she flew many times on Air Carrier Y and never had an issue with them not boarding it. I conferred with [the] Chief Pilot in ZZZ2 by phone and described the situation. Our Dangerous Goods expert in HQ called me and asked if we could get more information or a way to identify the battery. I called local maintenance and asked could they help by loosening the four hex bolts on the power area which they did. We looked the cart up on Store X website and all it identified was that it was Airline Approved." After opening the closed compartment; we followed the leads to a flat area and opened two more screws where a blue LI battery was located and had 'Hb Li-battery' identifier. Air Carrier X doesn't allow carts checked in cargo compartment with an attached LI battery. The battery must be unattached and carried in cabin only. Our maintenance was able to unhook the battery; secure the containers on the cart and tag the leads. We checked the cart in the cargo hold; and bagged the battery and carried it in cabin. Air Carrier X then notified ZZZ1 and ZZZ3; the final destination; to expect this cart and when it arrived in ZZZ3 to reinstall the battery. Air Carrier X coordinated with the flights and stations involved. I would like to flag this as a possible safety issue as Store X is selling these carts as airline approved; but no markings to allow airlines to comply with the procedures for Dangerous Goods. There is also no easy access to the battery to unattached. Since she stated she's flown many times with no issue or being questioned; seems to imply there were safety issues at the other flights with the cart being checked with a large LI battery in the cargo pit. Air Carrier X has had instances of batteries catching fire and if it is in the cargo it has potential to cause an accident or safety incident."