Replacement Shutter Release Button for E-PM1
Call the service shop directly and see if they will sell you the parts.
If not, I guess you could make one for short term. The same thing happened to me 12-13 years ago when I still used an Olympus compact 35mm. Button fell out but it could be activated with paper clip.
I took a push pin, one of those thumb tacks for a bulletin board that has a plastic head. Shortened the pin and rounded it off. Fashioned the head into a half dome. Held on with tape. Here's a picture. It did happen.
If you don't like this, I can understand. The auto-closing lens cap also fell off that camera. It still worked when I retired it though, around 2001.