If you looking for an eassy way to do this try to use the following script:

SET PAGESIZE 10000
SET feedback OFF
SET heading OFF
SET echo OFF
spool d:\SQL.OUT

SELECT TEXT
FROM USER_SOURCE
WHERE NAME = 'MY_PACKAGE';

spool OFF
SET echo ON
SET feedback ON
SET heading ON

CONNECT OTHER_USER/OTHER_PASSWORD@OTHER_DATABASE;

@d:\SQL.OUT