Just as a little text correction:
Should read
In later versions of elasticsearch you could use reindex from remote, but it is not available in version 2.4.0.
Reindex from remote was added in 5.0 of Elasticsearch: Reindex API | Elasticsearch Guide [5.0] | Elastic, so if "server B" is or can be version 5.x, then you could use this. I would encourage you to consider upgrading to 5.x or 6.x whenever possible regardless of this particular technical hurdle because of ongoing performance, functionality, and security improvements.
Anyway, presuming 5.x or 6.x is not an option in your case, @luiz.santos's solution is a good one!