Graphic Styles are the easiest method moving forward with new files.
If you have a bunch of existing files, and want to copy an appearance, you can still use Graphic Styles in perhaps an easier way.
There's no easy, automated, method to apply an appearance to a collection of files, so either way you will need to "touch" each asset file.
- Take your existing element with the shadow and drag it to the Graphic Styles panel.
- Now merely
Edit > Copy the element. (You can close the file now)
- Open a different asset file
- Select the new asset and then click the style in the Graphic Styles Panel.
The copy/pasting places the Graphic style you want into the newly opened file, then deleting the copied asset removes the actual artwork.
This is merely a shortcut to moving a Graphic Style between files without having to use a bunch of menu tracking to load files.
Be aware, grouping the artwork and then applying the shadow, and then making the Graphic Style is the procedure I would follow. Then upon opening old assets, select and group, then apply the Style. Graphic Styles actually have 2 forms - groups and individual objects. You can't tell them apart other than how they may or may not work with an object/group. So by making everything a group first, you ensure the style will work the same with everything.