So you're trying to transfer records within a table from database to another, but the table in the second database has more fields than the table in the first database.
The best way would to be to export the data from the first table with a full "INSERT INTO table (field1, field2, field3) VALUES ('data1', 'data2', 'data3');" SQL statement.
Then copy and paste these statements into the second database and run them. As long as the field names and data types match, you shouldn't have a problem.
If the additional fields defined in the table the information is being traferred to are marked as required/not null, you will need to set a default value.