Problem - 2 domains 1 shop

[epiepi]

I have 2 domains, for example:

www.mysite.com
www.myshop.com

I instaled a prestashop in subfolder www.mysite.com/myshop


www.myshop.com is redirected to www.mysite.com/myshop

and I Have following problem:
When I opening a product site http://www.mysite.com/myshop/product.php?id_product=116'>http://www.mysite.com/myshop/product.php?id_product=116 everything is ok, but if i want open www.myshop.com/product.php?id_product=116 which should be redirected I getting as reply:

http://www.mysite.com/myshop/product.php
with info: Product not found

Probably is something wrong with cookie, but i don't know what and how to resolve it...

[tomerg3]

It's not a good idea to have 2 URLs pointing to the same shop, search engines will detect it as 100% duplicate data and will penalize you.

The best practice is to pick a "default" URL and redirect the 2nd one to it.