Moving data from one database to another database with auto incriment keys
Just follow this... steps

These are the tables for database1

    create table if not exists table1 (
      id int(11) auto_increment,
      data1 varchar(50),
      primary key(id)
    );
    create table if not exists table2 (
      id int(11) auto_increment,
      data2 varchar(50),
      primary key(id)
    );
    create table if not exists table3 (
      id int(11) auto_increment,
      t1_id int(11),
      t2_id int(11),
      data3 varchar(50),
      primary key(id)
    );


There are the tables for  database2

    create table if not exists 2table1 (
      id int(11) auto_increment,
      data1 varchar(50),
      primary key(id)
    );
    create table if not exists 2table2 (
      id int(11) auto_increment,
      data2 varchar(50),
      primary key(id)
    );
    create table if not exists 2table3 (
      id int(11) auto_increment,
      t1_id int(11),
      t2_id int(11),
      data3 varchar(50),
      primary key(id)
    );


Here we have temp data for database1

    insert into database1.table1 (data1)
        values('table_1_data_1'),
        ('table_1_data_2'),
        ('table_1_data_3');

    insert into database1.table2 (data2)
        values('table_2_data_1'),
        ('table_2_data_2'),
        ('table_2_data_3');

    insert into database1.table3 (data3,t1_id,t2_id)
        values('table_3_data_1',1,1),
        ('table_3_data_2',1,2),
        ('table_3_data_3',2,1),
        ('table_3_data_4',2,2),
        ('table_3_data_5',2,3);


temp data for database2

    insert into database2.2table1 (data1)
        values('2table_1_data_1'),
        ('2table_1_data_2'),
        ('2table_1_data_3');

    insert into database2.2table2 (data2)
        values('2table_2_data_1'),
        ('2table_2_data_2'),
        ('2table_2_data_3');


Now come to the point

Here we are copying data
from database1s table1 to database2s 2table1

and

from database1s table2 to database2s 2table2

    insert into database2.2table1 (data1)
        select data1 from database1.table1;
    insert into database2.2table2 (data2)
        select data2 from database1.table2;


Now we are going to insert data into database2s 2table3

    insert into database2.2table3 (t1_id,t2_id,data3) select
      (select 2t1.id from database2.2table1 2t1 where 2t1.data1 =t1.data1 ),
      (select 2t2.id from database2.2table2 2t2 where 2t2.data2 =t2.data2 ),
      t3.data3
    from database1.table3 t3
    left join database1.table1 as t1 on t1.id = t3.t1_id
    left join database1.table2 as t2 on t2.id = t3.t2_id;


I hope it helps...