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It’s really easy if the turned pinion shoulder fits into the new escape wheel without having to open the hole. Really lucky too!
The pinion is held in place by a light press fit (edit here – and rivet!) and can be removed by placing the wheel on the staking set table and putting the pinion into a hole that is close fitting. You can then tap it out of the wheel. It will come out easily. You should see that the shoulder is cut into the pinion leaves just shy of the dedendum minor dia. So you should see a tiny bit of the leaves left on the arbor. This helps bite into the escape wheel hub and helps keep it from loosening up and rotating. You’ll probably find that the replacement wheel likely has a higher shoulder (hub) than the original wheel and may need to be turned or ground down a little after pressing in the pinion arbor to allow for clearance for the pivot shoulder to reach all the way through. This is also important as you don’t want the wheel to ride on the hub but rather the pivot shoulder.
If you need to open the hole a little and have questions about it please let me know.