Hi Artyom,
From the output you included I see that the first 3 objects were successfully copied and then you got the 403 error while trying to copy the fourth object. It sounds like you may not have read access to this fourth object. That might happen, for example, if two different projects copied files into that bucket, without specifying any ACLs, which by default would mean the object was ACL'd project-private to that second project.
If that's what happened here, you will need to add your identity as one of the project members allowed to read the object (or you could just re-upload to that object, with an ACL permitting you read access). You might also consider setting a default object ACL on the bucket, that allows each of the projects to read the objects in that bucket.
Mike