aS Cleaning Nozzle Trumpet

Just connect this gadget to a garden hose and to the mouthpiece receiver and open the tap!
To clean each valve slide, push the respective valve.
The usual house pressure will not damage anything and is enough to dissolve any contaminant like stale saliva (let it run for a while).
If I had a compressor, I would blow air into it to dry it. Then oil it.

Of course, this does not replace a thorough cleaning with a full disassembly of the instrument from time to time with detergent and brushes etc..

Also the felts may get wet. They may be taken out before, but if so, beware the valves are in their respective position or there may be a blockage of the water flow if they are out of their normal place which could push the slides out unintentionally.