Translation:Have you seen her book?
My Chinese friend said that 看见了 implies that 看见 has happened so it is weird then to make it a question with 吗. It sounds somewhat odd/contradictory. In other words, 你看见了她的书吗 is like "You have seen her book... have you?" Whereas if you move the 了 to the end of the sentence (你看见她的书了吗), then the 看见 is NOT implied to have already happened so it truly becomes a question, "Have you seen her book?"
You totally could put 了 right after the verb, which is how Duo usually does it. When I began studying Chinese, where to put 了 was one of the hardest things because there was a disconnect between what our textbook was telling us and what I'd hear speakers actually doing. I asked several different teachers and nearly all of them wound up saying, "It really depends on how it sounds best..."
"How it sounds best" usually means some combination of "we do it for rhythm," "we do it to make real-time understanding easier," and "we do it for complicated reasons that I have no conscious knowledge of." I've said it when teaching English. I'm not proud of that, but it's a thing teachers sometimes have to do.
了 is a complicated grammar point, and textbooks usually oversimplify those for two reasons, one good and one bad.
The good reason is that a beginner can't learn the main point if it's smothered in complicated details, or totally disconnected from any familiar grammar.
The bad reason is that the author relies too heavily on the comparison to familiar grammar, instead of taking the target language on its own terms.
As textbook explanations go, this is a pretty good one: https://eastasiastudent.net/china/mandarin/four-kinds-le/ Chao & Yang say pretty much the same thing in "A dictionary of spoken Chinese."
Li & Thompson, "Mandarin Chinese: A functional reference grammar," fixes the bad oversimplification. Their discussion is lonnnnnng, but to summarize: 了 after verb marks bounded action, not necessarily completed action. 了 after sentence marks a currently relevant situation, not necessarily a change of situation.
Yip & Rimmington, "Basic Chinese: A grammar and workbook," starts to fix the good oversimplification by noting that 'sounds bad' if there is no modifier for the object, so native speakers will add a second 了. And if you want a whole lot of details like that, their "Intermediate Chinese" has plenty more.
One reason le is not right after the verb in this sentence construction is because the sentence is not asking whether you have seen her book in a general sense; the question means the person is looking for her book and wonders whether you know where it is, because you have seen it. In this construction, the le goes at the end, right before ma.
见 is one of those curious words without an exact English counterpart. In some ways it works to show the completed action of seeing (看见) or hearing (听见), but it also is used to express meeting someone 我们在门口见面吧 ("let's meet at the gate"). I've never seen it used alone in the context of seeing something, as you suggest.
So, the 了 after the subject is the kind that indicates a recent change of state, rather than the completion of an action. If so, is this question implicitly saying "Have you seen her book (recently)?"
Would “你最近看见了她的书吗？” also be correct in spirit? Or perhaps completion is implied, then "你最近看见她的书吗"?