Data replication between SQL Server 2016 and SQL Server 2008 R2 is valid?
I'm afraid Replication between 2016 and 2008 is deprecated per Microsoft.
MSDN Link


  Replication is supported if each SQL Server endpoint is within two
  major versions of the current version of SQL Server. Consequently, SQL
  Server 2016 does not support replication to or from SQL Server 2008 or
  SQL Server 2008 R2.