While removing my fuel pump, i found that the mount stem that goes into the engine is snapped off. The remaining bit is still in the engine. Is this a problem? Should I get a new one?

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" Is this a problem? "

mmm....... yes and no

While not ideal, it still does its job.
To get it out will be a bugger.
1. Split the case and knock it out
2. tap into it and pull it out

the trouble with 2 is the debris caused going into the sump.

i would grind a bit off the top piece so it doesnt rub

the bottom piece wont fall in as it is tapered.

I will still "guide" the push rod - just a gap in the middle.

You could try and "hook" it out but I doubt it will come easily

Run a tap into it and use a bolt to pull it out,this is a fairly common problem in the volksie engines and this method has been used for over 60 years,load the thread of the tap with grease ro pick up the swarf and minimal swarf should go into the engine.

I would think you should get a new one - have a couple here in Brisbane

getting a new one is easy

getting the old one out is the problem

try wedging the shaft onto the broken bit with a sharp toothpick or two...the harder ones
I can give u a spare repl.