Simply put, you can’t really tell if it’s original, batteries suppliers like Simplo or Dynapak don’t work just for Apple and there’s plenty of B/C grades batteries with nice Apple logo stamped on them not delivering the same standards. However, your description would make me think you got a good quality battery and chances are it’s an original one. Easiest way to check battery health is downloading Coconut battery, a great tool to tell battery condition in just a screenshot.