Translation:Have you seen my cell phone?
I found this explanation for the placement of 了: https://www.chineseboost.com/grammar/le-grammar-summary/
Basically when you see 了 at the end of the phrase it means CHANGE OF STATE. In the current phrase I think it means if you have seen my cell phone now that I am looking for it and not in general some other undefined time.
If the sentence was 你看见了我的手机吗? I think it would be a case of ACTION COMPLETION and it would mean something like did you see my mobile phone (some time in the undefined past)? In which case we could answer something like "Yeah, you showed it to me last month when you first bought it" but this is not what the person who lost their cell phone is asking.
Please correct me if I am wrong.
This explains it pretty well.
“Have you seen my mobile?” should be accepted. We use it frequently in the UK.
Why is “了” placed after the object noun here and not following the verb “看见” in this instance?
To me, to say the sentence without "le" would mean the translation above. But with "le" around, I would think the person is asking: have you seen my cellphone already?
I didnt have formal training in Chinese though.
It’s important because it signifies past tense. Otherwise, it would be “Do you see my phone?”.