Old Letter is an item in the “Plot advancement” category (Key Items).
In-game descriptions
| Sword / Shield | A letter entrusted to you by a girl, to be delivered to a boy. Strangely, it looks old to you. |
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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