What is the difference between in receipt, on receipt and upon receipt?

I got the following message from a book store:

I am extremely sorry for this lapse as I hurriedly sent you the book to reach you on time when I received the book from the Publisher. I will certainly ask for the replacement and would send you a fresh book. Please return the book to the following address on receipt of the fresh book

and I googled "on receipt" just to be 100% sure that I understood the message right. My googling resulted seeing examples like "in receipt" and "upon receipt". What is the difference between the three:

• on receipt
• in receipt
• upon receipt

or are they all synonyms? As for the message that I got from the book store, doesn't it mean that when I get the new book, I can return the old book? :)

Thank you for your help! English isn't my native language and that's why I'm not always sure about the meaning x)

"On receipt" and "Upon receipt" would be synonymous (I suppose there is a minor grammatical difference, but in daily use you could use either) for "On receiving".

So, "on receipt of the fresh book" simply means "when you receive the fresh book".

"In receipt" doesn't fit here. It's not common usage, but it could be used to say "I am in receipt of the book" to mean "I have received the book"