It sounds pretty good to me. I can think of two changes I'd make to it. To be honest, however, I don't know if the two changes are right. :) "The history of cooperation and communication among BRICS countries can also be considered a history of cultural exchange, leading to communication and integration between different cultures." I switched around "also" and "be" and removed "as" between "considered" and "a". To me that sounds more natural, though, as I've said, I'm not 100% sure that it's grammatically correct. EDIT: Upon re-reading it, I thought it sounded slightly better by removing the "the" before "communication and integration".

The history of cooperation and communication between the BRICS countries can just as well be considered as that of a cultural exchange, leading to a higher level of their integration, independent of cultural differences.

Don't think it need rephrasing, it's authentic alright.