how to Grant Permission on a table to a user on the other database in oracle
Oracle article about Create database link:
To access a remote schema object, you must be granted access to the remote object in the remote database.

That means you need to grant the privileges locally (to the database on which they are) to the user as whom a user connect via the database link.

So, for example, if the database link was created like so

create database link DB_LINK 
connect to TESTUSER 
identified by PASSTHEWORD
using ...




then you have to 

grant all on a.tablename to TESTUSER;