After some research, as of today, it is not easy to change one S3 bucket from one user to another. I have found this solution:
and this other one using a proprietary solution http://support.bucketexplorer.com/topic1165.html
But could not implement it, since I don’t understand well how the IAM works.
So I went for the simplest way: delete the original bucket and create a new one with the same name
Warning: you will have to wait to have the name released.
If you try to create a new bucket with the same name right after you delete it, you will receive the warning:
A conflicting conditional operation is currently in progress against this resource. Please try again.