I already commented on a lot of grammar before in chat; thus, I'll keep it to story details. Make sure to reread your story for errors.
needed to be refilled very rarely.
I'm wondering how a magic pen is refilled.
In a week you will receive a full reimbursement
A reimbursement for a pen…?
In the same few sentences he had proved all of my suspitions…
**In a few sentences, he had proved all of my suspicions…
JUDGEMENT
I feel slightly wary of the progression of the start of the story, and I'm not entirely bought into how the narrator simply goes along with the policeman instead of asking for a badge specifically. To me, it'd make more sense if the policeman also threatened the narrator in some form. What are your thoughts on this? I like the dialogue that's already here though, so I'm confident you can come up with something.
In general, I like the second half, but it's lacking in a lot of energy and emotion, of which I would at least expect some. It is the Wanderer's Library after all, that he got invited to. Another concern I have is the ending, with the words outside of the quote box. I'm not sure if they're needed honestly, and they seem like quite a stretch, from patron to archivist without any hint as to what happened.
There are quite a few errors that persist here, so please read thoroughly again; if you want, I can list them out for you, but I would prefer if you try as well. Make sure to give credit to your reviewers.