Start dragging the file in Finder, then press ⌘Tab and choose the full-screen app; drop the file into it.
Switch to the app mid-drag
- Start dragging the file in Finder and keep holding.
- Press ⌘Tab and choose the full-screen app. macOS switches to its space.
- Drop the file into the app.
With dragand
dragand never comes in over a full-screen app, but its shortcuts still work there. Drop the file on the shelf before you switch, then press ⌃⌥⌘S in the full-screen app and drag it out.