I found both expressions -
the more common one is "he is on his honeymoon" - as in ON vacation ??

but it's also seen in many places where people use "he is in his honeymoon" - as in "in the middle of his honeymoon" ??

a set usage ? 

do you say " he died in his honeymoon " or " he died on his honeymoon " ? (i'd choose the former)

do you say " he died while he was in his honeymoon " or " he died while he was on his honeymoon " ? (i'd choose the latter)

do you say " a woman in her honeymoon is happier than ..." or " a woman on her honeymoon is happier than" (i'd choose the former)

Can anyone please explain the differences ? thanks
I can't explain the difference because I've never heard or used "in (one's) honeymoon". Emotion: smile
I am very surprised that anyone uses "in". And in such cases, right or wrong, I just assume it's British English. Emotion: smile
The important thing is that he died happy.
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I have never seen someone use "in" when referring to a honeymoon unless they are saying something like "the couple is still in their honeymoon stage" meaning that they are still very happy and very loving because they have not had any arguments or problems yet.

In all of the examples you gave above I would have chosen the word "on" to complete the sentence.
"In the middle of their honeymoon" is fine (because "in the middle" is a perfectly normal phrase); "in their honeymoon" is entirely different, and not idiomatic.
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 Avangi's reply was promoted to an answer.
funny that all respondents speak AmE - coincident ?