I am Prestashop expert and Prestashop certified, I have top level experience in prestashop architecture.
Here is what you will get from my service:
+Import old Prestashop product
+ Import Customer
+Import Image
+Import Category
+ Import other part of the shop

And here goes the explanation :

I will import your old prestashop database 1.5 to prestashop 1.6+ site.
Import images also.