You could adjust the "Fill" amount for the layer to 0, then save the remaining shadow as a (partially transparent) PNG file.
Layer>Layer Style>Create Layer - This will place the style on its own layer and clip it to the original layer. (This is assuming that the inner shadow was created with a layer style. If the shadow is part of the original image, then this won't work)
Layer>Layer Style>Create Layer
Thank you, Silkrooster, as I have somehow never noticed that menu entry before. Gotta love Photoshop - after almost 20 years I still learn new things every day.
You're welcome. Its kind of hard not to learn something. Have a Merry Christmas...
Yes. It is like discovering that one's spouse of 20 years, has a cute little dimple, that you never noticed before... Hardly a day goes by, that I do not learn something here too - might be a new feature, or perhaps just one that I never knew about. Makes for a great life.
But this "rasterizes" the Blending Options effect, yes placing it on it's own layer BUT removing all parameters editability found in the Layer Style dialogue.
Plus, I've experience strange buggy behavior trying to edit layes created with 'Create Layer(s)'. And not all resultant layers will be clipped to the parent layer such as Drop Shadows - depends on the Blending Option.
I still prefer Noel's method. Max editability.
If editability is a concern, then might as well leave it alone. There is no reason why the style can not be copied to another document or layer. Alt-dragging works wonders in these cases.
Something else the OP can try is take the original layer, convert to a smart object then appy a layer style to it. You can then replace the image inside of the smart object with any other image (preferably the same width and height) then save to web.
Because you can save a layer style, it is just as simple to create an action that will apply that style to the current layer, and run that action as part of a batch or image processor script, which would then apply that layerstyle to an entire folder of images.
Do a test on the action as I did not test it other than to verify that an action can apply a style.
There is always more than one way to skin a cat.