Mistakes with objective pronouns often occur when we have to choose between you and me and you and I. Because you is the same in both the subjective and the objective case, people get confused about I and me. The way to check this is to remove the second-person pronoun.
When he’s finished reading the book, he’ll give it to you or I .
If the sentence read “…he’ll give it to I,” we would know that “I” is wrong.
When he’s finished reading the book, he’ll give it to you or me .