The thing about "built in" FCP templates is that they are, in fact, **inside** the FCP app. It is so not recommended going into the application and moving these templates out of the app or even moving them from category to category inside the app.
For all those templates that do not offer the "Open a copy in Motion" option: these are functions written into the core code of FCP (InternalFiltersXPC.pluginkit) and there are no template files available. Others are Keyer, Luma Keyer, Draw Mask, etc.
If you want a "copy" of Drop Shadow placed in another category folder, simply Apply it to any Clip, then Save Effects Preset. Deselect any *other* effects in the pop-up dialog that you won't want with this preset and give it a Name (it can be the same but I suggest you make it slightly different) and change the Category to the one you want.
HTH