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