B737-900 Flight Attendant reported the Customer Service Agent erroneously informed the flight crew that a non-removable Lithium Ion powered wheelchair was approved for transport in cabin. After unsuccessful attempts to remove the battery; the wheelchair was left behind with customer approval.

Narrative

The Captain and I; the A FA; were informed by the CSA (Customer Service Agent) that a passenger had a lithium battery powered wheel chair that was legal to fly on the aircraft but wanted to make sure we were comfortable with it. After the passenger boarded the aircraft and we placed the wheelchair in the closet; we realized that the battery was not removable. After the Captain and I both consulted our manuals and he contacted flight ops; we informed the CSA of the issue. After most of the passengers were boarded and the flow of traffic cleared; both CSAs and two supervisors met the passenger and explained the safety issue. After making efforts to remove the battery that were unsuccessful; the passenger agreed to continue on the flight and leave the wheelchair behind. They were understanding and I thanked them for their cooperation. We also compensated the passenger and made sure there was a wheelchair provided for them upon arrival. I did not check the manual for requirements of a lithium powered battery wheelchair until the passenger was already boarding the aircraft I should have brought it up to look during my briefing with the CSA so I could verify myself that it was compliant and the issue could be resolved up at the gate with minimal delay.Double check manuals information; good communication with the F/D helped to catch and resolve the safety concern.