Air carrier Captain reported the crew had difficulty determining if a LiFePO4 battery could be transported in the cargo compartment or in the overhead compartment. It was determined it was safe to transport the battery in the overhead compartment.

Narrative

During boarding the Ops Agent handed us a LiFePO4" battery with IATA labeled documentation that was removed from an assistive device and asked us if we wanted it installed back onto the device and placed in the cargo compartment or placed in the overhead compartment. We dug into the FOM and found a note that states "Wheelchairs or assistive devices that contain lithium metal batteries are prohibited." A quick online search states that LiFePO4 batteries are a type of lithium-ion battery that contain iron phosphate. There-in lies the question. Does that make it a "lithium metal" battery and therefore prohibited? Continuing; reference to online states that they are a "safer and more stable" type of lithium-ion battery. The IATA labeled document that came with the battery was confusing and vague at best and ultimately not helpful. We called Dispatch and asked for a three-way conversation with the operations Chief Pilot. We discussed the issue fully; including referencing the table and determined that since the battery was less than 300Wh; 288 in this case; if it could be determined not to be a "lithium metal" battery we were ok to take it as carryon luggage. He brought in another person to the call who referenced the hazmat manual that had contradictory information from the FOM; but ultimately thought we were good to take the battery as well. As a side note there was discussion about whether or not this battery should be considered "non-spillable" because it was labeled as such; but again another note in the FOM states; "Lithium-ion batteries are not considered as Non-spillable or Dry sealed batteries." To say that the waters are muddied here is an understatement. We also included the flight attendants in the discussion to include whether or not the battery would fit in the LiFePO bag that they have in the back and determined it would fit; should it overheat in flight. Ultimately; we all agreed it was safe to take as carryon and placed in the overhead bin. The question still remains. What is considered a "lithium metal" battery?Suggestions: More complete information in both the FOM and hazmat manual that details what is and isn't considered lithium metal would be helpful. Also; removing contradictory(or at the very least ambiguously misleading) information from the hazmat vs FOM manuals would be helpful as well."