This artifact can be found during the section "Beyond the Wall", just after Joel and Tess' first encounter with three of the infected. Right before dropping down into the open air from up the staircase, go through the large hole in a wall to the left, and straight across the room will be a door. Go through the door and in the upper far left corner will be a table - the artifact is on top of it, alongside a consumable health item.
Note: All punctuation and capitalization are typed up as it appears in the game, when you choose to read it in text-form.
We were so close. I'm sitting outside the walls
knowing I'll never see the inside of the zone.
While waiting for the smuggler to show up, we
heard a squad of soldiers approaching. In our
panic, we ducked into this building in hopes of
hiding from them. None of us noticed the spores
until it was too late. We're all infected - we have
a few hours, maybe a day at most. I hope the
smuggler is still coming so that I can at least
pass this note to you.
I should've listened to you and come to the zone
with you when I had the chance. Now it's too
- Joel: They got infected trying to sneak into the zone.
- Tess: Tsh. As much as everyone complains about it. You got all these poor bastards wishing they were living on the inside.