I had a book request for a hardcover book but when I went to mail the book, I discovered that the spine was cracked. So I PM the requestor and asked if they still wanted it. They did not. The book was removed the book from my bookshelf. I can't remember now if I removed it or if the system removed it.

Anyway, I later glued the cracked spine and the book seems fine now. The crack is not noticable anymore. Nor is the glue job apparent.

Can I repost the book to my bookshelf now that it has been mended?

I think if the book looks fine and doesn't look like a book with a reglued spine it should be fine to post. If its apparent that unpostable damage was repaired, then I wouldn't post it.

Thank you for your help. I will repost it.

I'm not sure I would post it.  How do you know that the glue is going to hold.  Could be it gets jostled around in shipping and by the time it gets to the recipient the glue may have let go - and then you will have a RWAP. 

I wouldn't repost it.  I repair books as part of my job and unless you are a professional people can tell if the book has been reglued.
I dont post any books that I have repaired because I know the book was once damaged and seen as unpostable.

And depending on what glue you used could meant it could cause the spine to break enroute if its cold. Book glue needs to be flexible for it work correctly and not cause more issues for the spine. (just an FYI for the future.)