I would like to know whether the following is correct or should be improved:
John will stand in for me in my absence over the next week and half.
I am especially unsure about the preposition (over).
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The part "over the next week and a half" is fine. But I'd change the "in my absence". to "during my absence".
John will stand in for me during my absence over the next week and half.
Because "in my absence" could mean it's not a certainty that you are absent. But considering you are specifying a time period, it does not play together that well in my opinion.
In my absence, you should contact John.
Which would mean that in case you are absent, John is the "go-to" person. It does not mean that you will be absent.
Your sentence is good as written. In this case, you are using over to mean during. There's nothing wrong with it.