what you want to do is not possible to do it with automatic tools or modules.
The reason is you will have registers in tables with same id, even with other fields with same information, it's very complex what you want to do, and the only way to do it is with a person who know type code and make a personal script, but in my opinion very complex, because you must to make several changes on tables.
In my opinion the way to do it is something like this:
1. First you have to update old shop from 1.4 to 1.6
2. Second you have to get last id of tables like ps_products, ps_customers and ps_orders from new shop, once you have id's you have to change all id_product, id_customer and id_order from regarding tables in old shop, begining from next number that you have got from new shop. for example, if last id_customer in 1.6 shop is 932 your first id_customer in old shop must to be 933. obviously you must to change all id_customer of every table which have relation with ps_customer to dont brake relation between tables, and same work with orders, products, etc...
3. Third Pray to expect both databases had same structure, in that case you can move all data to final shop. ( i will not explain how to do it, is too long)
It's possible to do it? YES
It's complex to do it? YES IT IS!
Can you find people to do it? YES, but will not be cheap, if you want more info, please MP.