Most of the time botrytis affects the entire thickness of the petal, and the spot is seen front and back.
Botrytis spores are everywhere. It is impossible to keep them off your plants. There is no reason to remove the flowers, nor the stem. Doing so will not keep the fungus off other plants.
Botrytis prefers being wet and cool, which is not what Phals like. Keep the flowers warmer and don't let them get wet, and you will minimize botrytis problems.
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