Cable release broke in shutter release

[Kirks518]

Some shutter button assemblies simply screw off (like the F3). This gives access to the release socket which is basically just a threaded hole with a connecting rod and spring inside. I don't know the FM, but there is probably info online about dis-assembly that would indicate whether or not the button assembly comes off, or whether you need to remove the top plate. Either way, access to, and removal of the broken bit is likely to be easier with the parts removed. You should google FM repair, FM top plate removal, etc to see what you get.
Alex

This.

According to the repair manual (LINK TO PDF HERE), on page F1 (12), the shutter button cover should unscrew, and you can then access the underside of the shutter button, and (theoretically) you should be able to remove it from the back side. If not, just purchase a new shutter button, or a donor parts body, and replace the button.

If you have difficulty getting a grip on the button cover, get a rubber band or similar grippy-rubber-thingy, and have a go at it.