Yes Renee. It is not about the connector, but its about permissions in Oracle.
Think of this as sql statement, in which you are pulling information from one schema and updating in another schema.
As per my understanding, you first need to provide read privilege on schema A table, something like this "grant select on A.table1 to B".
Then, test your update script in schema B. If it works fine, plug in as postscript.
Hope this helps.
~Thanks
Jatinder