Basic watchmaking tips - crystal fitting

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Archer,

I obtained the Omega tool and a crystal and gasket. When you replace the crystal do you do it with the movement inside the case or is it best to remove it? I can see it would be very difficult to alight the tachymeter scale without the dial.

Also, the grease is applied to the inside of the tool where the crystal is, or is it applied to the outer perimeter of the tool?

Thanks for the help!
The movement is mounted in the case when I do it - as you say that's really the best way to make sure it's properly lined up with the dial.

The inside of the tool is greased.