Professor’s Mask is an item in the “Plot advancement” category (Key Items).
In-game descriptions
| Sun / Moon · Ultra Sun / Ultra Moon · Let’s Go, Pikachu! / Let’s Go, Eevee! · Sword / Shield | The mask that belongs to The Masked Royal. This pro wrestler apparently sews his mask on a machine himself. |
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Where to find it
Not placed on the atlas maps (so far: Red/Blue and Generation 3).
Sources : PokeAPI (items, item_flavor_text, machines) · atlas · pokeemerald species_info.h