Yes and No.This flash terminal cap required to maintain the weather-sealing of the camera, right? And any flash terminal cap will do?
While any cap will fit, what is important is not the fit to the standard flash terminal itself, but the screw thread outside that holds the cap in place and makes it water resistant.
Many caps are basic push-ons.
What you need is screw-on, with the right screw dimensions.
I have just tried swapping the caps between the EM1-I and the EM1-II and can confirm they are an identical fit. The only difference is that the EM1-I has a little flash sign marked on it.
We already know the EM1-III has the same fit as the EM1-II, so all three models are identical.